I have to connect to the MBNA website from a browser, not from within Quicken directly. (This is for an old MBNA line of credit account. I realize MBNA is now Bank of America, so it's possible BoA customers and/or MBNA credit card customers have different access from what I'm describing.)
For several weeks, I've had trouble downloading statements from there. Then it dawned on me. I've been using a beta version of the upcoming Internet Explorer 7. So, I tried using the Opera browser, which I also have on my computer and -- presto -- the statements downloaded without a problem. I don't know if it's a version 7 problem or if the problem is with all versions of IE.
Anyway, just a note of information that if you have access to another browser, you might try it if you're having trouble downloading data files for Quicken from websites