As already discussed, when you exit while enroute between cities, you start the trip over from that city again.
When it's convenient, I travel to the next city on the map, press ESC, and exit the game. Especially if I'm chasing a thief; sometimes, a couple days later when I play again, I forget to check whether I have a sundisk--and he gets away. Also, it keeps me from having to do the "You've finished the region" level again if applicable.
I am not sure I agree with the fact that you start the route over. I have left part way through (a path not in the middle of a game) and come back to the same place, only having to complete one or two screens for the one path. However, I have never left when chasing a thief. Perhaps then that might happen.
I also haven't had a lot of the problems that some have had. (knocks on wood!)