Is your output on this problematic network similar to the following :
$ telnet mirrors.usc.edu 873
Connected to hpc-mirror.usc.edu.
Escape character is '^]'.
Also, what happens if you add -n (--dry-run) to the following command :
> rsync -artv rsync://mirrors.usc.edu/centos/5.6/updates/i386/RPMS/ --exclude=debug/ /var/www/html/centos/5/updates/i386
If it is working on from networks (which it seems to be) then I suspect there is a problem with the connection.
Is the firewall opened for connections on port 873 to all systems on the internet? The reason I ask is because you could start an iperf <http://iperf.sourceforge.net/> server (operating on port 863) on a remote system and see if connections works from the problematic network/host and what kind of throughput you are getting. Perhaps the connection opens but once data starts being passed something is going wrong?
The other thing is that you could setup an rsync server on a different system and see if it has the same problem. With such a test you should see the same issue if it is a network issue.
As far as I am able to see the mirror you are connecting to for the source seems to be working fine <mirrors.usc.edu>. I suspect there is an issue with the network connection or host.
Check the environment variables on the system for anything which may be causing issues. Also, you if possible you could try building a copy of rsync from source and see if that helps?
Finally, have you attempted the same rsync command from another system within the problematic network? If so what was the result did it manage to pull the data down from the server?
Hopefully, at least some of the information above is helpful =<:^)