I'm not seeing the pop-up stay, but this is reported by users every once in a while. That pop-up is completely controlled by Facebook, unfortunately, and we don't have the ability to close it. We can't simply poke into that window because it could contain authentication data, and that's not something Facebook (rightfully) trusts us with.
However, there's a few things you can try:
1) Close Chrome down completely and restart it - This should clear session data and hopefully fix the problem
2) Clear all cache/browser history in Chrome
3) Try another browser, just to see if the pop-up still remains
4) Try another Facebook account.
I tested on your site in Chrome (on a Mac just now and Win7 earlier today when I confirmed the issue) and the pop-up went away every time as expected. Usually, this is a transient bug on Facebook's part either associated with your computer or user. It's usually not something that every users sees.. though, that's been a bug that Facebook's had in the past...
Good luck, and we like to see progress too!
P.S. I forgot, during testing, I disabled the caching in the System->Global Configuration area. I didn't re-enable it, and I downgrade my user to Registered so I can't fix it. Just wanted to let you know.