Iphone keeps asking me for my AppleID password

My iPhone keeps asking me for my AppleID password.

This usually happens after I wake the phone and/or start any app. The problem is intermittent (and too consistant that it has become very annoying!)

This started happening about 1.5 weeks ago.

I called into Apple support and they don't have any idea of how to fix it other than me backing up my phone and performing a brand new restore. I haven't done that yet as it seems to be a brute force approach (and lengthy timewise at that).

From what I can remember, I purchased a song from my iPhone using the iTunes store. Ever since then, it has started asking me for my password for my AppleID. If I enter the password and click OK, everything is fine, but after a few moments, it will ask me for my password again. Also, if I hit Cancel, everything is fine, and again, it will ask me for my AppleID password.

I have the lastest build/version of iOS 5.0.1 installed. The password entered IS correct. I am able to purchase music/movies/tv shows from my AppleTV with the same AppleID and password. I have verified on my iPhone under settings, Itunes that my AppleID is correct as well.

Anybody else getting this and/or have a solution?