Defeated simply means that, defeated. The whole point of spell card duel system is so that the participants don't die from it.
Besides, Flandre does have after-battle dialogue, unlike Rumia or Wriggle. (which didn't die either, but they're pretty beat) The liitle insane vampire has enough stamina (I'm sure) to play a danmaku battle and live. (It uses the Hakurei spell-card system, which is a safe way of using one's powers in a way that won't kill anyone, unless they're that stupid.) Also, she's a vampire. She's immortal. I'm sure "even if she has a little bat left", she can indeed regenerate anyway. Most youkai can.
No, defeat means to be cleared.