When all of the party members are afflicted with any of the statuses that prevent action, (ie. Paralysis, Confuse, Sleep) the battle will freeze and stop progressing. The battle camera still moves around, and the idle animations still play, but the battle stops right there, with a blank battle message. 

This only occurs when everyone in the party is affected by a status that prevents action. Instead of the status effects taking place like normal, nothing happens and the battle gets stuck right there.

In the above images, the "?" icon represents the "Confused" status, while the bolt icon represents the "Paralyzed" status. The 'GGs' grave-looking icon represents the "KO" status. It sits like this until I 'ALT + F4' the whole window. No key presses or mouse clicks do anything. I can't seem to find anyone else talking about this sort of situation.

It's like in Pokemon when your team is asleep and you have to just watch them get whittled down by Dream Eater.