Hi Teresa,
This sounds strange -- we've tried to duplicate the problem and haven't had any luck so far. That is, when we're busy typing a message to a guest in the web staffing client and a new chat comes in pinned, we don't lose the text we're typing. Also, the focus doesn't switch, so the typing cursor stays on the original chat.
So if you're seeing your text disappear when a new chat comes in pinned, can you let us know what browser/version you're in so we can do some more testing?
We do know of one issue where composed-but-not-sent messages will disappear, and that happens when the user goes to another tab within the web client (like Activity). This is in our development tracker for attention. But it's not related to the proactive pinning of new chats.