iTunes 9 won't quit asking for my password.

I watch a lot of TV shows on iTunes, and I've never had a problem like this before. Ever since I upgraded to iTunes 9, after each episode finishes, it wants me to put in my password several times, and it won't start downloading the next episode until I do. Sometimes I have to sign in 4 or 5 times in a row, and then it takes me to the "Apple Account Information" page of the iTunes store -- even though I never clicked on it.

It's a big problem, because my connection is a slow one and I usually leave the computer on at night or when I'm at work, but now it keeps stopping after each download to ask for my password, and it won't start the next episode unitl I do.