I've been experiencing this for awhile, but only recently testing it.
On mobile browser, Chrome functionality for the in-game messenger seems buggy. I've started using Firefox with success though. I'm running Android 5.0.2 with HTC 4.25.651.18.
The issue with Chrome is you cannot be the first person in a game to send a message. It won't process after hitting send and deletes what is typed. If a message has been posted, you need to hit send 2-3 times and then delete any extras that pop up. I don't think it's a huge issue especially because there is a work around. Just seemed worth mentioning.
Is what's happening to you anything similar to this?
http://www.wargear.net/forum/showthread/4127/Cant_send_game_messages
Sort of? It doesn't allow me to be the first person in game to send a message. Public or private, its almost like it needs to be initialized. Then it goes to that problem in that thread.
FYI, this bug has been reproduced in house. A fix is in the works, but no ETA on a solution at this point.
Finally fixed - a very weird one, it was caused by the textarea resizing when you entered text which meant when the Send button was pressed it just moved the button instead of actually submitting.
Really weird, glad it could be fixed and thank you!