LAN List does not populate reliably

I have reopened this ticket, specifically referring to the lack of a LAN list in the Multiplayer menu. Direct connect does work in my tests. I have included some notes from MC-98499 here:

Nothing shows up in the multiplayer menu. It is possible to select "Direct Connect" in the multiplayer menu, enter the IP address of the local game, and enter the game that way. But still nothing is listed under "Scanning for games on local network." With 2 of the 4 computers, the behaviour is as expected and the games show up. With the other 2, they can host the game and be seen by the 2 correctly functioning computers, but not by each other. When the version is switched back to 1.8.9, all the 4 computers can host and detect LAN games as usual. This problem is specific to 1.9.