I have a Lumia 920 running 8.1 Update, Developer Preview, Black.
I used to have Straight Talk (AT&T) but recently switched to Airvoice (AT&T) and started to have the problem. I just tried to the Group MMS off/power cycle/on strategy... hopefully fixes it (temporarily...?)
So, the common thread between all of its is still AT&T.
From what I've experienced so far, the "fix" that we've been using does indeed work temporarily. Usually, after anywhere from 5 to 7 days, the issue will show up again. I've recently been fixing my issue the following way with the same temporary results. It's a little quicker than our original "fix".
1. Delete the problem text message.
2. In settings, turn off group messaging.
3. Power off/on phone.
4. In settings, turn group messaging back on.