We used to have a problem with chat whenever someone was hosting on our on-campus network. They would type, click enter, and it wouldn't appear. You had to refresh the browser to refresh chat, and usually then, it was on delay.
Before I took over, it was so bad that our volunteers were no longer even hosting on site, so when I took over our Online Campus we started looking into it a little more in depth (We did fix the problem, but we've stayed with the model of volunteers being able to host off site anyway, especially now that we have volunteers from other states and countries).
That was a while ago, and a different problem than you're having but here's what our IT guru said fixed ours:
The problem then was cross site scripting (XSS) between ChurchOnline and a service called Pubnub, which was hosting part of the chat room back end.
Most firewalls should block XSS by default, as it used to be a really popular way to hack a computer (before firewalls started blocking it). In this case you have to enable it to make the chat room work.
It’s really important that people not completely disable XSS blocking on their firewall, but specifically for the CurchOnline and Pubnub connection.
So hopefully that helps! I don't understand that world, but trust our Tech team, and the problem has been fixed.