Since the professional warriors of the time were generally obligated to perform a set amount of military service on a yearly basis for their liege (I've heard 40 days per year mentioned as a common contractual obligation), and the rest of any given army would be comprised of levied peasants who had crops and animals to tend to, what happened when a conflict became drawn out and the army had to remain on campaign for extended periods of time?

For example, one lord declares war on his neighbor, seeking to press a claim on his land and is assuming a quick victory. However, upon reaching the enemy lord's castle, a lengthy, protracted siege takes place that lasts, say, three months or longer. The war began in Summer but now it is the Fall and time for the harvest.

On one hand, you have the knights and nobles of the army, who have already given their required service for the year by now, and on the other hand, you have thousands of farmers who's crops aren't being harvested sitting in your siege camp.

What do you do as the commanding lord at this point to both keep your army in the field and prevent your economy from being decimated by keeping much of the workforce away for too long?