Server issues should now be resolved, thank you for your patience! Continue reading if you'd like to hear the long version...
In the previous update to Kreedz Climbing, the game's Steamworks implementation was updated to the newest version - this was necessary to allow the Workshop's Playtime Tracking feature to work. This involves updating the game's steam_api dll.
Unfortunately I don't have access to the source code of srcds.exe (the dedicated server executable), so I couldn't update it's usage of Steamworks. The result is that the new steam_api dll was not compatible and causing the server to be unable to use Steam features (causing it to be forced into LAN mode).
The solution was that now the game technically uses two versions of Steamworks at once - the server uses the old version and the client uses the newer one. This is extremely weird but also unfortunately necessary.
You might be wondering how this issue got into a live patch - all of Kreedz Climbing's updates are thoroughly tested on both the game and the dedicated server, however things were a bit weird here - I test these updates on my own computer which has Steam installed. If Steam is installed on a server machine, the server connects to that instead of using it's local copy. The local copy wasn't compatible with the steam_api dll update, but Steam itself was! That's why the dedicated server works for me, but didn't work for many standalone server machines.
And that's why most of the servers weren't working! And that's the weird solution that fixed it. A big thank you to Zord for bringing this to my attention, and I'd like to remind everyone that if you ever have any issues, let me know on the forum and I'll do my best to fix it!
Happy climbing!