Well, it appears that the bug that reset my missions and such recently is reproducible. At least, I ran the battery down to zero again yesterday while playing, and everything except possessions and coin count was lost again.
This is especially annoying as I had beaten my personal best again on the iPad (not by a lot; something like 8400 instead of 8100, but it's still irritating). At least I hadn't put any effort into achievements since the first reset.
Anyway, if you have an iPad 2 (this has never happened with my iPhone, although I haven't run that down since the latest upgrade), even with the latest version of the game, it looks like you better not run the battery all the way down. And now I've checked; syncing the iPad right afterwards doesn't help either.
The picture is the profile page, afterwards. Note the picture of the avatar, the coin count, and the best score. Time to get in touch with Halfbrick, I guess.