We've changed our SSL setup a bit.
In response to Microsoft's broken implementation of SSLv3 in some versions of Internet Explorer, we had turned SSLv3 off entirely.
However, there are a few people out there on the internet who have (for one reason or another) changed their browser settings to ONLY use SSLv3. Because SSL connections happen before browser information is sent, there was no way to only disable SSLv3 for these specific IE versions.
To fix problems with these users, we've made the SSL configuration only turn off the specific SSLv3 ciphers that Microsoft fudged. We've also turned on the SSLSessionCache (because these versions of IE assume that you use caching).
[Edit] Dissabling SSL3 support in IE appears to have fixed my access problems.