So, it turns out that if both you and your date run out of cards at the same time, but you have more health, the game gets stuck. Players can't win by card-out.
Yes, my suggestion is to use the game's back button and try to avoid causing that scenario to happen. There's also logic but that happens when both sides hit 0 at the same time during boss battles (unsure what happens during SMS dates) but I'd try and avoid that too. It has been fixed for 0.08 though.
I'll see if I can fix it sometime later tonight though.