I know this is super late notice, but I just wanted to let you know that I encountered the exact same thing today on my iPad 2. Mailbox has always worked for me until today. This compose message glitch occured and I found your post in my attempts to find a fix.
I sent a bug report to the Mailbox team from the in-app support with a screenshot showing the message body field being grayed out with my keyboard missing. As for now, there is nothing we can do.
Just wanted to let you know that you are not alone in this. If I find anything or hear back, I'll update.