2nd Update: It worked for a while, but during those two days I couldn't read all the messages in some of the conversations. The first message of a certain user was visible completely in the right window. The beginning of the last message is visible in the small left window. But I can't see any of the messages inbetween. This happens only with some of the conversations, not all of them.
My test message from yesterday went through alright, and I received an answer today, both of which I could read. Then, a few minutes ago, as I tried to answer it, -- poof! -- all was gone, and the error message appeared "Your browser is not supported."
*Edit*: Using Safari on MacBook Pro