I went through the hoops with some bloke from Apple, and it worked for a couple of days, now, whenever I logon, I get the same message as you. They had me sign out of the Store, sign back in, delete some cache material in a couple of preferences, which all sounded very professional - to no result.
My solution, which was really, really radical, was to signout of iTunes and have nothingto do with it!
Of course, this means that I can't download anything from the iTunes store, but that's no big problem.
In comment, it's a crying shame that a company I've been buying computer equipment from since 1993 can't be bothered to put the resources into fixing this little problem; I don't think they realise how irritating it is to have iTunes wailing away that it needs my password again and again and again. I can live without the iTunes store.
This is probably no help at all, but I've gone down the road with Apple engineers; I have AppleCare coverage, and they should do better. They can't and it seems like they don't care.
I'd be interested if you get a more than 2 day fix!