I like the answers posted so far. I have had a number of experiences related to dice frustration. There's been the table of mostly engaged players except for that guy that gets mad whenever he doesn't cleave an orcs head in every time he tries. We don't play with that guy anymore. Then there's the engaging mid-level campaign where everyone is starting to get frustrated because they've invested time from level 0 in the campaign and like it but the dynamics of their characters don't make sense anymore and everyone wishes they go could go back and change something critical at level 1. That stands out especially related to dice rolls, but usually doesn't happen often since the players are already experienced and I take time especially with new players to make sure they create a balanced addition to the party. The most experience I have with this seems related to your experience, however. Most of the time when this happens, even if the players are trying to stay engaged and are not necessarily being immature or unreasonable and are just frustrated, it's due to what appears to be cursed math and nothing more (or a prankster Kilroy has defiled all our dice). A particular example that stands out was the straw that tried to break the party's back in the form of a displacer beast that magically enjoyed uncanny good fortune when trying to displace itself and avoid physical attacks and nearly destroyed the entire party. This was after several sessions where attacks that barely needed checks would result in the player rolling a 1 or the previous band of orcs getting multiple critical hits and avoiding attacks that they really shouldn't have had much chance to avoid.
I pulled a plot deus ex machina out of thin air to explain the mishap with the displacer beast. A trusted NPC that had been questing with the party was able to identify a curse on the party that had been negatively influencing the party's luck. With some non-combat effort, they were able to remove the curse. For the next few battles that occurred immediately after, I informed the players of depreciating bonuses to all their rolls. It started with +3 during the first encounter and went away at the rate of 1 each new encounter. This was explained as the characters feeling like they were suddenly extra lucky for a short time due to the psychological effects of the curse's immediate removal. By the time the bonuses wore off, everyone mostly rolled an expected balance of results except for a last couple straggling botches by this one guy that has since burnt those dies and purchased new dice. The players expressed this was a fun way of temporarily distracting from dice frustration without unbalancing the characters permanently or sending monsters that weren't any challenge.
Another thing that I have done in the past is keep a secret log of roleplaying that players do and use that to reward particularly unlucky rolls all without the players knowing I do that. I award a special type of experience for roleplaying that the players do not know about on a scale of 1-5. 1 means they at least tried but just not very well or in depth, 5 means they did homework and spent time researching topics in between sessions or sacrificed a great deal for the purpose of roleplay. One of my players intentionally had her character become problematic for her party to persuade her character to board a large seafaring vessel for the next leg of the quest. We hadn't discussed why her character didn't have any points in Swim in character creation, but over time she developed a fear of large bodies of water due to a tragic childhood accident. The quest was delayed nearly to disaster, and I secretly awarded her character 5 roleplaying points. I have different triggers for how the points are redeemed (again, without the players knowing about all this):
Start of a session. I roll for each player to determine how much of their built-up secret roleplay experience points they will spend this session. This depends on how long the campaign has been going, but is generally between 1 and 10 of their points but no more than half their remaining points. If they will be spending more than 5 points, I spend 5 of those points to throw in special magic items that will be in the loot of the session designed best for that character's body type and class (what the party does with it is a different story, though).
For dice rolls. I reserve the remaining points that will be spent by that player to distribute throughout the night to that character converted into secret bonuses, secret negative modifiers to targeted enemies, extra clues, and the occasional "I'm sorry, I didn't see that roll.. can you roll it again? hint hint, cough cough" for an exceptionally bad string of rolls. The players think the latter is done to save the storyline so we aren't rerolling new characters every week, but in fact it's due to a systematic approach of rewarding their roleplaying.
More notes on the deus ex machina. In addition, if everyone's having a rough time with dice rolls but everyone has a good bank built up of secret roleplaying experience points, I may elect to spend more of the players' points they have in reserve to activate the cavalry riding in at just the right time or the evil gnome tinkerer's weapon of moderately-massive destruction suddenly has a critical structural failure and starts collapsing which distracts the evil gnome's henchman and gives the party the upperhand again.
This is a pretty systematic approach that might work better for me than you, but ultimately I believe in ditching the rules for the sake of the storyline. If the players make reasonable decisions that just turn out bad due to unruly gambler's fallacy and the lack of infinite hit points and they are altogether great roleplayers, I try to assess how to relieve frustration without unbalancing the game. If the cavalry makes sense, send them in. If they can survive even though they'll end up losing ground in their quest and a few prized possessions and we can find meaning and a satisfying way to overcome the obstacles within a few sessions, I will make them roll with the punches of bad rolls.
Another approach that can work is to simply change gears. Give the players some shore leave, let them pursue some of their characters' bucket lists for new and strange places when there isn't an immediate crisis going on. Ultimately, I think dice frustration when there are a lot of uncanny bad rolls can be rooted in a loss of control. If overlooking bad rolls or sending in the reinforcements doesn't make sense, reroute the story for a couple days in-game time. Cut the dungeon crawl short, get them back into town or in a new place, and make sure the players know there is nothing to do but wait for a couple days. Give them enough time to prepare for the next leg of the quest, but give them way too much time to prepare. If they have a brief but unavoidable period of nothing to do but pace and twiddle thumbs for their characters, they'll likely go exploring to do unrelated shopping and pursue character development interactions with townfolk. The rogue may finally have time to try and create her first set of Masterwork lock picks with some good tools from a friendly or unsuspecting smith's shop. The cleric may take some time to explore the art of cooking by experimenting with strange local flavors in a foreign land. The barbarian may want to stand drop-jawed all day in the weapon surplus store engaged in battle story exchanges with the retired barbarian shopkeeper. Give them chances during this time to make skill checks that aren't quite so critical. So what if the cleric rolls a 1 cooking fish soup? OK, so that's a bad example. Maybe dissuade anyone from attempting advanced cooking that could result in poisoning the party if botched. But you get the idea.
It can be understandable for players to get frustrated. It really depends on you, your players, and your dice experience. It's inevitable that some RPG group somewhere in the world will eventually roll thirty or more 1's in one gaming session. In one game where I myself was a player with four other players, all five of us proceeded to get a critical hit each in succession of another. Initiative determined that the enemy went last, but the enemy didn't get to do that. Things would have been challenging as it turns out, we found from our DM who spent three minutes staring at the table in what could only be described as awe and disgust. Upon being attacked, the enemy would have activated a contingency of powerful magic effects and summoned cohorts for an epic battle. They didn't get the chance because we weren't supposed to do that much damage in the first round before the enemy could act. It turned a very powerful and nefarious "boss" fight into an anti-climax of curb-stomping the enemy immediately. It goes both ways, and that's reflective of real life. Sometimes, the final boss is a pushover. Sometimes, the peon manages to whack you in the back of the head just the right way to knock you out even though you were a blackbelt when the peon was in diapers. It happens.
If it's a reasonable crew, make accommodations that somehow make sense, don't unbalance the game, don't convey that the players can expect such whenever they are frustrated, but also restore satisfaction to the game. If it's a reasonable crew and there are not very unlucky dice rolls and only merely consistently unfortunate rolls in minor and moderate ways, try the solutions in other answers, too. If the players seem too quick to walk away when they fail rolls more than seems to be average, remind them of math and that they need to roll with the punches or consider a different game to relieve stress.
One last thought here is that I once DM'ed a dice-less version of Dungeons and Dragons for a group as a collaborative experiment. We created stats and continued to level up, but this was more to gauge and help give a mental assessment of each character. We based what happened on common sense rules. If a clumsy character tried to hit an enemy with a rock, it usually didn't happen as they would have liked. If a skilled paladin was trying to smash in a low-level mob's head, they usually did with no problem. I would occasionally make a random judgment call to mimic an expected and reasonable average of probability related to scores and who should be able to do what how many times out of a hundred. Generally, everything was using a modified "take 10" system. If it was reasonable to auto-pass, they usually would. If they were overextending themselves, I'd let them succeed part of the time and fail part of the time. I'd spit out random hit point values when needed, trying to not show favor to particular low or high ends. This approach was interesting for a simple and quick mini-game, but not something I would do for a whole campaign. However, this approach can be used temporarily in a standard game if everyone is getting bad rolls and they are becoming frustrated. Just switch the dice rolls off and play it by ear using common sense. They probably aren't going to critical much if at all and are going to get hit sometimes and only sometimes hit an even match. The rogue might be better at this than the wizard.
Best of luck, and whatever you do don't try microwaving everyone's dice so that 1's are avoided. It doesn't work well, makes the dice ugly, and ruins your burritos forever in that microwave.