This issue is still on our plate.
One thing I'd like you to try...
Go to Settings > General Settings... and change the 'Message Editor Interface' from Enhanced Interface to Basic Editor.
Save the changes and let me know if this helps...
Um, not sure where that setting is. There is no Settings>General Settings anywhere that I can find.
Not sure if it helps, but I noticed the same problem with another forum, e-cigarette-forum.com. Maybe it's the same forum software and there is an issue between WP and that.
One other thing I noticed, at least on the other forum, if I'm not logged in and I click "Reply with Quote", which makes me log in, then I can type a post normally without keyboard issues. Any attempt to post after that and the issue returns.
Edit: Never mind, I realised you were talking about forum settings, not phone settings. I made the change, it was set to standard and I changed it to basic. Didn't seem to help any though.
I don't know if it is related, but my screen "jumps" every few seconds when I browse this site on my phone. Not sure if it is the ads or what. Maybe it makes the keyboard retract.