I am also surprised that this outage of Continental.com has been going on so long.
I logged a ticket (via continental.com web-form) on 30-May around 10PM.
I was trying to research B-fares to HKG. I have been receiving (variously) 'File not found', 'Gateway timed out', and just plain old 404 errors since that time.
(In addition to times when I just cannot logon to my OnePass username...)

The response to my ticket was that I should call 800-300-1547 to book my travel.

One (somewhat) interesting thing I noted was that at some point there is a long timeout while my browser is trying to access a site named 'p-as01.estara.com' . This site never responds, and I was thinking "hmm estara, E-Star Alliance, hmm"... but then I visited estara.com and saw that it concerns the 'click-to-call / click-to-chat' application.