After going a few rounds with HostGator, here's what they have to say about this matter.
Hello,
We have looked over your configuration, our configuration, and our logs. As you noted, the issue only happens with the favicon.ico file, and works if you don't use the virtual multisite URL. After checking our Apache configuration, I found nothing specific to favicon.ico in any of our configuration files. I did find that this is a redirect problem, as shown with the following log entries:
# tail -f /etc/httpd/logs/error_log | grep 74.202.255.243
[Fri Jul 01 14:44:26 2011] [error] [client 74.202.255.243] Request exceeded the limit of 10 internal redirects due to probable configuration error. Use 'LimitInternalRecursion' to increase the limit if necessary. Use 'LogLevel debug' to get a backtrace.
[Fri Jul 01 14:44:26 2011] [error] [client 74.202.255.243] Request exceeded the limit of 10 internal redirects due to probable configuration error. Use 'LimitInternalRecursion' to increase the limit if necessary. Use 'LogLevel debug' to get a backtrace.
As you know, WordPress handles nearly all of it's redirects internally, and WordPress does not appear to be functioning correctly when redirecting the favicon.ico and only favicon.ico. At this point, this is a WordPress issue that we are unable to assist. We recommend consulting a third-party developer through a site such as http://elance.com. Please note that if you would like to us to turn on LogLevel debug for Apache, as noted in the error, we will be unable to do that at this time, as this generates far too many log entries and can cause unnecessary load on our shared servers.
You are also welcome to review our VPS and Dedicated servers, which do allow this level of debugging and customization to assist with problems relating to scripts. You can review our offerings at:
http://hostgator.com
If you have any issues or concerns that we may assist, please let us know, and we'll be happy to do so.
Jason [last name removed]
Linux Systems Administrator
HostGator.com LLC