Never mind. I got lucky and found the problem I think. After posting I happened to read about others having similar problems and tried deleting a book that I had recently uploaded to my Kindle. Whatever the problem was, deleting the book seems to have cleared it because it hasn't started rebooting by itself again. I had tried restarting it thinking that maybe something didn't reboot properly recently and that didn't clear it, but apparently the Kindle just didn't like one of the books I'd loaded onto it.
