There are several implications to letting players redo an encounter, but I'll focus on a few important ones.
Con - You lose the element of surprise
Players and characters alike generally don't know what is ahead of them. This is a very important tool for you as a DM, no matter what you're trying to accomplish. When players go back in, the encounter is not as good as it was the first time, since they know what is going to happen. The best part of any story or encounter is not knowing what might happen.
Con - Players are more likely to meta-game in this encounter
A hard part about role-playing is only using information your characters know. It becomes easy when the players know as much about a situation as a character does. But now, the players know about an encounter their characters do not. They will be tempted to use this information, and you need to make sure they're aware of this possibility. You may not care if they meta game, it is up to you.
Pro - Players will be able to choose to act differently
A redo is a strong thing. We all wish we could go back in time and change the way we handled certain situations. A redo is giving your players that opportunity. Maybe this time they will be diplomatic (if possible) or they may find more information by talking to the enemy. Is this bad or good? That's up to you and what you're trying to accomplish.
Con - You as DM lose out on opportunities to tell a story
Your players' characters have died. Or have they? This is a great opportunity for you to do some DM magic and tell a compelling and interesting story. There are so many things you can do besides letting them be dead. You can strip them of all their things and put them in a prison (yay, a new adventure!). You can resurrect them by some foul magic and give them temporary or permanent side effects. You can let them re-roll characters to later discover their old characters' corpses. The possibilities are endless! You lose this opportunity when you allow a redo. Be aware of that.
Pro - You gain a different opportunity to tell a story
As user902383 has pointed out, a redo can also be an opportunity to tell a story. If you should redo, you can make it part of the campaign story, rather than an out of character decision. Make it a Groundhog Day type of situation. Whatever you decide to do, it would be in your best interest to spin a story out of it.
Con - Randomness
You mentioned he failed a save by 1 and that, had he updated his sheet, he would not have. There is no telling that he will survive this redo. He might just lose outright and the redo might be a complete waste of time. Not only that, but if they do fail the redo, they'll feel even more frustrated about it.
Should I give them a redo?
This is hard for any of us to say. It depends heavily on what kind of campaign you're running. If you're trying to kill your players, a redo is a big setback for you. If you're trying to tell a story, redoing an encounter might not be a big deal. Personally, it seems kinda sloppy, but such slop can be forgiven for new players and new DMs as you learn to play (if indeed you or they are new). I wouldn't let this type of thing happen more than once. I do think it's okay to redo a single turn if someone realizes they forgot something. Example, your player remembers their saves are different the next turn, so you give them a success and replay the turn from there. But after a session is over is just too far.
Out of game, as others have mentioned, they need to be up to date on their own character sheets. You can give them a mulligan if you want, but again, I wouldn't let it be a reoccurring thing. This can be a good learning experience without the sting of defeat. However, as you can see, the biggest implications seem to be cons rather than pros.