It seems clicking on a server invitation thing for KF rarely works. Thankfully there's a reliable method available.

When you get an invite, copy the server IP in the chat box, open the command console and just type this:

open (paste)

Press enter and if there's an vacant slot, you should be able to join every time.

Its actually a Killing Floor reference from the Simpsons many years before KF even existed.

https://www.youtube.com/watch?v=8f2P5yJFQKw