Ok, as a frequent user of JAvalon these days thanks to my computer going caput some time ago, here are my thoughts:
JAvalon does not have triggers.
JAvalon has no timeout feature. You can sit in the BB all day if you want as long as your internet connection isn't cut off by your computer going to sleep or something.
Now, JAvalon does suck when you're actually trying to do things. *Sometimes* it cuts out when you're using MAPS at panic speed to get someplace. This would go along with Yorik's claim of it dc-ing during automated tasks, as using maps is effectively an automated task.
If it disconnects when you aren't using it, I think that's just your internet connection, Yorik, as I sit on the bb for copious amounts of time myself with no problem.
Regardless, whenever there's a problem, you should tell Genesis about it and let him know what's going on. He's told me before that he's interested in all potential problems with JAvalon so that it runs smoothly for new people trying out the game.

Hope that helps some!
