In my particular area of specialty, the Crusades, siege lengths were primarily determined by the willingness and motivation of the besieged populace and the garrison to hold out, not necessarily by breaches in the walls or the strength of opposing numbers (though these did affect the motivation of the defenders). Throughout this period a sequence of 1) Encirclement and 2) protracted assaults followed by 3) besiegers breaching the walls and 4) successfully entering the gaps and 5) overcoming the defenders is exceedingly rare compared to the number of fortified cities and castles captured total in this period. That's because going through an entire siege is very costly for the attackers and very dangerous for the defenders. When a castle or city is successfully assaulted, it would typically result in the death or enslavement of all inside and certainly the forfeiture of all of their wealth. For that reason, if defenders saw that they had a low probability of winning the siege, or a very low probability of a relief force reaching them and lifting the siege, they would typically make quick provisions for their surrender. Defenders without hope would usually not hold out just because they could. Likewise, attackers would be hesitant to attack a well-fortified city (or one with easy access to reinforcements) or would only briefly siege it in order to try and secure a quick surrender or find a defector willing to assist them in entering. Siege weapons helped in this, but were rarely effective enough to be decisive.

For example, Kilij Arslan led a relief force to try and overcome the combined crusader/Byzantine forces besieging Nicea during the first crusade. After his defeat, there was no real hope of another relief force materializing and the defenders could see the siege weapons being readied. The inhabitants and garrison quickly surrendered to the Emperor rather than hold out during an assault that could have cost them their lives.

Countless sieges were determined because the attacker found an accomplice inside the city that was willing to let them in, in exchange for a bribe or other favorable treatment. This seems to have been more common when the defenders (or at least a portion of them) had similarities with the attackers. For that reason it is very common to hear of mass expulsions of potentially sympathetic populations from cities in advance of a siege. Defenders were understandably anxious to get rid of anyone in their ranks that could be convinced to seek favorable treatment from the attackers when the going got tough. Usually during the crusades this meant that Eastern Christians and Jews were distrusted by all sides.

As another example, Muslim historian Ibn al-Ithir reports that the siege of Antioch (1098) saw all the Orthodox Christians expelled from the city in advance of the siege, but even so, after a long and terrible siege, a disaffected Muslim armor-maker helped the Christians to enter the city through a disused tower.

You can read more in Christopher Tyerman's "God's War" or "The Crusades Through Arab Eyes" by Maalouf