Sounds strange for that to happen,
Specially if you can access vCOPS through the vi client (which uses the web login also) which im guessing is what your saying
When you isolate he second site are networks being dropped too? almost sounds like your having a network/routing or resolution issue over it being a problem with vCOPS.
I have 5 sites in link mode running vCOPS 5.7 and the only time I cant connect to the web login is when the UI server is down or not available, having a site offline makes no difference apart from the alarms in vCOPS