I would just make it so that your character counts as being "defeated" if at the end of the game they have a weakness with a game end effect in play.
The problem with this is that there are several of these weaknesses that take a minimum of 2 or 3 turns to clear regardless of the situation. This would force the players to stop trying to win the game if one of these cards shows up late in play.
I said a long time ago that I wished FFG would stop making these type of weaknesses. I find the ones that only affect the current game to be more thematic and less meta.