Proxy Cached

We encountered a very strange problem. We host a web site:
www.[our_site].com and a large number of our users belong to an
organization group with central network control and they can only
access our web site through two headquarter proxy servers: x.x.a.7 and
x.x.b.8, which was set in security dept of the group headquarter. The
web site was working fine till recently when those user accessing via
x.x.a.7 all have problem suddently while those accessing via x.x.b.8
have no problem. The users accessing via x.x.a.7 are directed to wrong
page, very slow response, hang on some page or encounter errors, etc.
If they access the same site via another alias, like
www2.[our_site].com which points to the same web server, they will not
have any problem. They do not have problem to access any other web
sites we tried, including our other web sites hosting in the same site,
even the same server. If the users change their ie setting to use other
public proxy server, they will have no problem to access our site.
Strict security policy are applied to the user site, so we cannot ping,
tracert or do any other network testing from user machine. Since user
has no problem to access any other web site, the headquarter security
department wont handle our case and simply think it is our problem.