The TVTropes Trope Finder is where you can come to ask questions like "Do we have this one?" and "What's the trope about...?" Trying to rediscover a long lost show or other medium but need a little help? Head to Media Finder and try your luck there. Want to propose a new trope? You should be over at You Know, That Thing Where.
If we drop the time travel part, that'd be Chronic Hero Syndrome and/or Samaritan Syndrome — that they try and try and try to save everyone, and fail and fail and fail not because they're inept, but because they're holding themselves to an impossible goal or standard.
I think one frequent outcome of excessive time travel is to be hounded by Clock Roaches, which would probably be stressful too.
Edited by KD
There's also Temporal Sickness if the act of time travel causes adverse side effects.
Exactly What It Says on the Tin.
Do we have a trope about time-travlleing characters who suffer mentally and/or physically due to the circumstances of their time-travel?
For example, they try and try to prevent the death of a loved one, but it always fails because You Can't Fight Fate?