My answer will demonstrate that human beings wear out very quickly in combat. When I say "combat" I don't mean standing behind cover and watching your enemy on the other side of the street, or being in the same grid square as enemy combatants, or marching across a field to engage the enemy while your cavalry units soften up the enemy lines. When I say "combat", I mean swinging your sword at your enemy, fighting to end the other guy's life in order to save your own, or grappling in the dirt with knives.
I assert that human beings cannot physically sustain hard combat for more than a short number of minutes. Anybody that thinks they can, I think has never had to fight, or trained for any physical activity as exhausting as combat sports. My answer will demonstrate that regardless of whether or not we have evidence of combat relief in historical battles (despite the fact that it does exist), that the lack of capacity for sustained combat in human beings would require that relief was provided in these battles. We may not know exactly how they relieved one another on the front lines, or how often, but I'll show you that it would have had to happen, and it would have had to happen fairly regularly, because even exceptional and legendary fighters wear out quickly in combat, on the order of minutes.
For my first trick, I'll use a comment under the answer to provide some actual evidence of what I'm saying: Combat sports and martial arts. Mixed martial arts (MMA) fighters are hand-to-hand combatants with no weapons and no armour fighting in ideal conditions: They're well-rested beforehand (e.g. no forced march, well-fed, ample time to sleep the night before), they're fit for the fight, and they've been training for sometimes years beforehand. This video demonstrates a trained fighter in a state of exhaustion at the start of the third round. MMA fights are individual rounds of five minutes (which is on the far end of round length in combat sports) with an entire minute between rounds to sit and rest. If humans can sustain long bouts of combat, why isn't this done in all of the various kinds of combat sports? The answer is because humans cannot sustain long bouts of combat, and rounds are broken by rest specifically because of this fact. I think it stretches credibility to try and say that human beings can sustain long stretches of combat, provided that every sport -- and especially combat sports -- provides short rounds broken by periods of rest for the competitors.
For example, here are the rules for UFC, a specific brand of mixed martial arts, which stipulates that even a championship match "is to be for 5 rounds, each round no more than 5 minutes duration, with a rest period of 1 minute between each round." Then take a look at this discussion about boxing on Wikipedia. In particular, they talk about the length of championship boxing match being between ten and fifteen rounds of a couple minutes each, with a full minute of rest between each of the rounds. Here are some rules for swordfighting matches, which specifies that the "round lasts for 60 seconds, 60 seconds rest between each
round." And here is the Wikipedia page for Combatives training, the hand-to-hand combat taught the US Army infantry soldiers, which provides a competition where the "fight consists of one ten-minute round."
Modern soldiers in combat use a couple of techniques to relieve one another from sustained combat, even while advancing on the enemy. One of those maneuvers is a flanking maneuver, which provides some relief to the soldiers on the immediate front while also pressing the advantage against the enemy: "Even when not entirely successful, for example at Anzio these operations can relieve pressure on troops on the main battle front, by forcing the enemy to divert resources to contain the new front." There is also what we in the infantry call "bounding" or "bounding overwatch", which allows a second soldier or group of soldiers to advance on an enemy position and take up a new fighting position, and thereby relieve the first soldier or group of soldiers and enable them to maneuver. These most basic infantry tactics have relief built directly into them.
And for my own touch of anecdote, since that seems to be totally acceptable, I was in the US Army infantry for twelve years and deployed four times, and I've spent most of my life training and competing in martial arts of various kinds. I have to say, if you think you're going to outlast any of these trained athletes or soldiers and sustain a hard fight for more than a handful of minutes at a time, you're in for a surprise. Regardless, I encourage you to get out there and take up martial arts (or join the army) and see for yourself! Fighting is hard.