Seemingly randomly, all players are disconnected from a server with a message reading "timed out". In the multiplayer server list, the numbers will appear to show these people still online, but when trying to connect to the server, the process will get stuck on the "encrypting" stage.
Only resolution is forcefully closing and restarting the server.
I was the server admin of the server that had this problem (twice). Server side, the server stopped responding to input (could not stop it with 'stop' command) and repeatedly gave "Username logged in with UUID X" messages, slowly, with the counter increasing each time.