You are correct in your assumption. Hand-to-hand combat is extremely fatiguing. I'm doubtful that any soldiers, medieval or otherwise, could fight actively for much more than fifteen or twenty minutes at a stretch without becoming totally blown, never mind nine hours. I subscribe to the "pulse" theory, which is to say that I think battles consisted of many smaller episodes of combat interspersed with periods of relative inactivity. Think of it as: attackers go forward, engage the enemy, fail to break their formation, spontaneously pull back, get their breath, reorganize their formation, and go forward again to try for a different result. In general, pre-gunpowder battles were won by breaking the enemy's morale and formation, not by immense face-to-face slaughter; the real killing occurred once the enemy was broken and fleeing. This is supported by the sources we have on the Battle of Hastings. The Normans seem to have attrited and worn down the English over the course of the day by a combination of long-range archery and feigned retreats to draw overeager soldiers from their shield wall; only defeating them as evening was coming on.

The problem with trying to establish a firm chronology for the Battle of Hastings lies with the sources. Medieval accounts are not anything like modern after action reports; they're just not that detailed or concerned with the nitty gritty. They go for the broad strokes and prioritize the dramatic acts of great men (one of whom is very often the writer's patron!) over the humdrum of tactics and organization. The opening of the battle, the first (genuine) retreat, and the Norman counterattack all probably occurred before noon; the feigned retreats and the breaking of the shield wall occurred later in the day.

You may find my posts in this thread of some interest: https://www.reddit.com/r/AskHistorians/comments/57cewr/how_did_william_the_bastardconqueror_raise_such_a/