Let's assume the situation of two combatants with decent armor, like maile, and longswords.
One of the combatants manages to get a sideways cut in to the hip or the ribcage. I would assume the hit hurts, but since we're not talking heavy weaponry here like an axe the padding should be able to prevent broken bones. Depending on the situation, the force of impact might bring the fighter of balance, or it might not. In the case that it doesn't, I wonder what the most proper reaction would be.
Jumping back to gather your senses and prepare for the next pass would seem like a decent option, but I guess it can be expected that the opponent will press on and throw his next blow pretty fast.
On the other hand, it might be a good moment to strike: the opponents weapon is out of the way for a moment, he is in good striking distance, so the situation seems good to bring in a better hit than he did.
Or might it be safer for the hit opponent to press in and close the distance, where he'll probably start to wrestle, but at least can assume that he won't take another blow immediately?
Of course it all depends on how much pain the blow caused (but I would expect expierienced fighters to be quite capable of ignoring a pretty large amount of momentary pain), the awareness and reaction time, so the question is pretty general.
I guess I should reformulate the question from the POV of the one striking the blow: How dangerous is the situation for him? Is it dangerous enough that it would be sensible to immediately leap into guard, or is a counter-attack in that moment unlikely enough to immediately launch a follow-up (assuming that the hit opponent isn't thrown off balance, in the other case the answer seems pretty obvious). Are there known instances that fighters deliberately took a blow on their armor in order to get into a better position for an immediate counter-attack?
