iPad keeps asking for password and rejects it!

[hpowders]

I have this maddening problem. My iPad 2 asks for my password when I log on and then rejects it. It prompts me to change my password which I've done 6 times already. What happens is the new password works for one day and then doesn't work the next day! I'm running out of passwords! Any ideas why this is happening? Why won't it store and remember any of my passwords?
Thanks!