Title. Absolutely no idea what causes this as sometimes it's already there when I first start the game, and other times it shows up between matches.
If nobody is typing in the chatbox the chatbox will go away to prevent screen clutter - maybe this is what you were experiencing?
I also had problems where the chat disappeared. When this happened i could still type a message but I was unable to see it or anything else like quick chat. I'm not even sure if my messages came through or were just not even send. It did fix itself after a few rounds when i suddenly was able to see it again.