From my own experience with Historic medieval Battle the main challenge is endurance and not strength. Most of my experience is from fighting with the long sword, a two handed sword which could be used one handed for single attacks. The weight of this type of weapon is approximately between 1.1kg (2.4 lb) and 1.8 kg (4.0 lb). Due to the good balance and the low weight holding the sword and using it for a few swings is no great feat. But after a while the strain is recognizable. The movements become less accurate and therefore, for training, the danger rises. Especially if armor(*) is added the point of exhaustion is reached even sooner. Depending on the temperature and humidity I would say that in the best case after 15 minutes of continuous battle I reach a point where it would be dangerous to continue (because of unprecise movements, not enough stopping power if a attack wasn't blocked).

It should be remarked that training session is definitely different from a real battle and that the rest of my training is more for strength than endurance.

(*) Armor in this case means a gambeson, helmet, chain armor for the upper body and leg and hand protection.