We've recently been hit by a major issue preventing players from playing on almost all of the ZPS servers. We've informed Valve and we're investigating the issue for any solutions. I'm trying to get in contact with the owners of the few servers that are working to see what they did that fixed it.
If you know how to fix the issue, please comment below. If you have any information on the issue you think could be helpful, comment or put a ticket into Valve yourself so that they can fix the problem as soon as possible.
Sorry for the inconvenience, we hope it won't be long before it's resolved so we can all go back to enjoying ZPS on our favorite servers!
EDIT:
From the few posts and what I've heard from someone else. Running the server as listen instead of dedicted seems to fix the issue. Not a solution but a temporary work around for those who would like to keep their servers up and population flowing.
(From viewing players' time on some of the working servers, it appears as if they aren't running as listen servers. If they were, we would be seeing someone connected for many more hours than everyone else and probably AFK'ing. Like on the ZG server for instance, player on for 75 hours indicating it's obviously a listen server. On Hayden's or Specialist's server I see players connected for ~2 1/2 hours, which tells me it's probably not a listen server. So the above work around may not be what they're doing to run their servers.)