The highest I've seen on a dyno (this is all on Heroku) is over a day, web #13 and #14 are on 22 hours now. I think they're actually eventually running out of memory or being retired and replaced by Heroku rather than crashing but I'm not sure, it's not being caught in the exception catching.
Most of the crashes come down to stupid things, it's so easy to make a mistake when you don't have a compiler watching your back. External dependencies can hurt if they're laggy or unavailable. Unterminated requests are a really easy accident as well.
At this point I just use exception catching and dump the results into Redis unless I'm specifically hunting down a bug and want the crash to occur:
http://api.playtomic.com/load.html