The point of sieges isn't to knock down the fortifications, it's to prevent supplies from entering the castle and forcing surrender before the population starves to death. Now if they have a year's worth of supplies that would make for a long siege, but it wouldn't be unheard of. Candia was sieged for 21 years.
Also if the only way into the castle is with a giant crane, you probably don't even need that big of an army to maintain the siege, so even a multiyear siege may not be too bad. Assuming the castle didn't have any allies that could come to it's defense.