This is incredibly difficult to debug since it seems non-deterministic and latency-sensitive. In particular latency issues are very thorny since simply setting a breakpoint in the debugger changes the latency and can cause issues to change :-
If you look in the browser console you can see it logging some errors about being unable to read data. I think it's failing to read data for some message, which causes it to fall back to an error path which means for some objects it considers it to have received no messages. In the multiplayer engine if an object does not receive data for ~3 seconds, it destroys it as presumably having timed out. So I think disappearing objects is caused by the timeout, and the real problem is being unable to read data. I've not been able to isolate it much further than that though. As ever producing an even smaller, simpler reproduction would help.