Medieval siege was a complex, highly choreographed process that ended with a castle assault only when other tactics had failed to force a surrender unless, of course, the attacking king or lord had a particular investment in breaking his opponent. Because the costs were so high, military leaders normally did not rush into a siege with Shakespeare-esque 'rushing into the breach' strategy.

Until about 1100, tactics mainly consisted of starving out the defenders by blockade. Many more sieges were settled by negotiation, bribery, or forms of intimidation than open warfare.

Most attacking armies knights and lords were only obliged to remain on campaign for roughly 40 days per year after which point they could leave or negotiate 'contracts' with their lords to extend their stay. Many attacking kings would carefully have to work out how many of their lords owe knight duty and how often reinforcements would come. At the end of the 40 day period attacking generals had to be very careful that they could muster reinforcements to replace their current knights or have enough coin for mercenaries.

With that being said many defenders knew that if they had enough food or water for at least 40 days that could potentially outlast the invading force or at least survive long enough for reinforcements to come.

How long seiges tended to last really varied. Was it a castle or town? How big? was it a little wooden frontier fort or was it an grand citadel? How well built were the defenses and how well manned? Did they have a water supply? How capable were the soldiers and officers on either side? There are really a lot of factors to take into consideration and biases in the answer to this question.

To simplify it though sieges couldn't lasted anywhere from weeks to years, with neither being an outlier. There were cases in the hundred year war where castles held for a couple of years. In the later medieval era Constantinople fell to the Ottomans in a space of weeks, though the ottomans had a HUGE numerical advantage. The answer really depends.

I'm just an armchair historian but i hope my answer shed some light.

A lot of this knowledge i just knew from over the years and cant really source but if you're looking for more reading check out this article. http://www.historynet.com/medieval-warfare-how-to-capture-a-castle-with-siegecraft.htm