In a few battles, especially in Muslims accounts, it is said that some battles last for 3 days or 4. Some examples are Siffin, Yermuk, and Qadissiyah. I have read researchers say that at max a man in armor can fight in melee for 40 minutes or so. And battle accounts in ancient times were quick affairs were the opposing army routes and is then massacred. So does this casts doubt into the accounts themselves or was it common when the opposing army does not route?
Ok, let me start by saying we don't really have any primary sources that break down how battles physically worked in detail. What we do have are models on how ancient combat may have worked out.
Those caveats aside, the model proposed by Roman scholar Adrian Goldsworthy suggests that soldiers didn't just fight it out for 40min straight and then be exhausted. The idea is that combat is scary and people don't just run willy-nilly into combat like you see in movies. Because of the fear of dying (no antibiotics, no Geneva convention, no painkillers) most soldiers will be fighting defensively - concentrating on protecting themselves more than getting a killing blow. There would be some who were aggressive, who were motivated and they'd be the ones likely doing the majority of the killing during the fighting. These people would be the Viking huscarls, Roman centurions, knights, etc...
The fighting would be in short spurts with the lines closing, led by the aggressive fighters, and after some minutes of hard fighting the lines would pull back as men became tired. They'd fall back just far enough that they'd be safe from an immediate attack. There they'd catch their breaths and psych themselves up for another round of combat. This cycle would continue until one army broke and then the vast majority of casualties would occur as the winners would strike the fighters down from behind. If neither side was particularly motivated, then they might spend a lot of time just standing there trying to get the courage to cross that last dozen or so meters into combat. Just screaming insults at the enemy, yelling encouragement, calling out to fellow soldiers, etc...
Now if neither army broke then it's possible that you could get multiple days of 'fighting'. Especially if it's in the winter when there's less hours of daylight.
As for ancient battles, they could be quick or could take all day. Now if one side has really shaky morale you get those 'tearless' battles where the army routs before even making contact. The best example to my area of knowledge is Allia where the Roman army collapsed when the Gauls charged.