So, I'll preface this by saying that I'm new to Fate (and tabletop RPGs in general) and would advise taking my advise with a grain of salt.

That said, I would first look at the way you're using advantages for your NPCs. Fiction First, right? So what are the NPCs trying to accomplish? In this case, it seems like after a while, this particular enemy would be willing to take some short-term damage in order to finally end the duel. So your NPC should be focusing on offensive advantages first, and only using overcomes when it's absolutely necessary, (such as overcoming an aspect that would prevent them from being able to attack.) Even if they have a free invoke that could be used defensively, they probably shouldn't use it except for an attack. If not using those would kill the NPC, they should only use the bare minimum to not die, and then strike back with everything else they've got left, maybe even spend a fate point to invoke their own consequences in this one last desperate attack.

Also, what kind of duel is this? Are they fighting to the death? If not, then maybe one party should concede the moment they take the first consequence, because they don't really want to die for a sport.

Alternatively, if you want, you could hack in some sort of fatigue mechanic. After you fight for so long your reaction time starts to slow. Each character gets a Fatigued aspect, and gets -2 to all defensive rolls for the rest of the scene.