One of the most important things for a DM to remember is to make failure interesting. Your players (and you) are there to have fun. Dying because you had a couple bad rolls isn't fun, it's just frustrating. And as you suggest, it's likely to discourage players.
That said, that doesn't mean that there should never be a risk of failure in your game. If there's no chance of failure, that's boring! Getting failure right is all about how the failure affects the entire party. So perhaps instead of the PC falling to their death, they fall into a deep pit, where they take some significant but non-crippling amount of damage upon landing - and are then confronted by something hungry in the darkness. That's interesting, because now the entire group has to make some choices: should the fallen PC try to climb back up before she's eaten, perhaps with assistance from the others? Should the others purposefully jump down to help her? Can they provide assistance against the grue from above, without getting themselves trapped? Or perhaps there's no grue, but the time it takes to extract the fallen PC from the pit means they don't reach the Dread Altar before the Necromancer finishes her Dire Ritual of Destruction. Etc. You can even use it as a chance to reward the players if they do something interesting after the failure: perhaps they find the body of another adventurer who also fell into the pit, who still has some useful gear; or they find a back door into the dungeon. Whatever keeps things exciting!
Basically, try to never kill a player just because they had two unlucky dice rolls. (Obviously there's some situations where that might still be appropriate, such as sudden-death dungeons like the Tomb of Horrors, or failing death saving throws in D&D 4e, but in most such situations the other PCs also have a chance to intervene before the unlucky rolls kill the character.) Instead, look for ways to make failure interesting by throwing additional challenges at the players, and reward them if they figure out a way to turn the failure into an advantage.