Twice, I've woken up to find most of my apps missing from my iPad for no apparent reason. They're just missing. Yesterday, I connected it to my computer and was able to get all the missing apps back but I don't want to have to deal with this every day.
I use my iPad as an alarm clock, leaving it plugged in with the alarm clock app open for eight or nine hours. Ive been dong this for several weeks, I don't know if that could be causing a problem.

Are you syncing with iCloud? I wonder if deleting apps on your PC and other devices are deleting them on your iPad. This shouldn't happen though.