The duration of a fight has nothing to do with your probabilities of being injured.
The nature of the attack does. If the attacker wants to kill, they will stab/shoot to kill. The aim is to kill the target and leave. If the hit fails, they will try again later. If the attacker's aim is to inflict pain, then they will only stop if either when they have inflicted enough damage (whatever that is) or they are taken out. In both those cases, expect the attacker to plan the ambush in such a way as no matter what the victims does, they cannot escape.
The skill of the attacker does. If the attacker is a wee mean drunk unable to stand, their attacks are not going to hurt. Just dodge. If the attacker is Chuck Norris... Well, we know how that ends. I heard that a rattle snake bit Chuck Norris and after three days of agony, the snake died.
The proximity to your mates does. If all your mates from the martial art club, marines, and special forces are a minute away, the longer the fight lasts the less chances you are to get hurt. You are more likely to get hurt in the first minute than the tenth!
Boxers, MMA, and other contact sport demonstrate this all the time: The longer a match last, the more injury? Nope. The longer a match last, the more the pair are evenly matched.
No! ItAct first, act fast is utter rubbish.