No solution -- just something similar seen on the Mac side. I'll try on the Windows side (also 7 & 64-bit) later on today and loop back if I run across anything relevant.
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For whatever it may be worth -- my experience with that popup on the Mac side:
I updated to iTunes 10.5.1 via Software Update late in the day on 11/15. iTunes then loaded once the update was done. I could see in the background that iTunes seemed to already have my Apple ID noted in the upper right-hand corner where it normally is, which I thought meant that it 'remembered' me and had me still logged in. Nevertheless, in front of iTunes, was a popup window asking me to log in to enable automatic downloads. It looked legitimate and I did sign in, thinking that I'd use iTunes Match eventually and figuring that the popup was an opt-in bit necessary for either Match or the 10.5.1 update itself. Then, after signing in, it brought up the same popup a second time. Er... It didn't seem to have any different language than the first, nor did it have a warning saying I'd fat-fingered my login the first time or the like. So, gritting my teeth, I signed in a second time.
That's the last I've seen of that popup asking to enable automatic downloads or the like. I've tried signing out within iTunes to see if the same popup about enabling automatic downloads would come back when I tried to sign in again -- nope. I've also tried signing in with an intentionally incorrect password -- and at least the normal Apple ID signin popup that's part of iTunes comes back with red text indicating there was a problem. Furthermore, now I'm wondering what that enabling automatic downloads popup was about since iTunes Match is something you need to subsequently purchase for $25 a year ... and when I look within Preferences -> Store, the Automatic Downloads section shows all three boxes unchecked (Music, Apps, Books).
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Anyhow, I too am looking forward to hearing what others have experienced -- hopefully there's an answer to the loop you are experiencing that doesn't involve backing up and re-installing iTunes from scratch or something similarly drastic.