Another bug report. This happened on both my record and my GFs at around the same point, just before the (minor spoiler) suicide bomber on the bridge:
Battles hang after inputting commands for the first round. Nobody takes any actions. The hang occurs if and only if (larger spoiler) Malayna is in the party. The presence of other members and party order don't seem to matter. Neither does the specific encounter. Removing her from the party prevents the hang, but it returns if we put her back in.
Our next-to-last saves (about an hour back) don't exhibit the issue. Looking through the comment thread, this may be the same bug reported by Intergalactic Trash about six months back. It's probably significant that all three cases happened at the same point in the game.
I'm afraid I updated the game before realizing you might want to know the version it occurred on, but I might be able to dig the previous one out of the download cache if you think it would be useful.
I can provide the faulty saves if it will be helpful for troubleshooting.