Not sure how to reproduce, but I was just in a state were a Saros session was open between Alice and Bob. Alice's chat messages would be received by Bob, but no new chat messages would be displayed in Alice's chat view, not even the ones sent by herself. So she's connected to the right room, but something with the listener doesn't work.
Reopening the session would fix it, but it would probably also work to just close and reopen the chat view.
Apparently it can just stop working in the middle of a running session.
Bob's view:
[alice1_fu (16:04)]: asdf
[alice1_fu (16:04)]: hm
[alice1_fu (16:04)]: asdf
[alice1_fu (16:04)]: asdf
[alice1_fu (16:04)]: asdf
Alice's view (host) of the same "discussion":
[You (16:04)]: asdf
[You (16:04)]: hm
The chat got an complete overhaul with 13.3.29 so it is not likely that this bug still exist.