Smuggling in a few dozen troops? Plausible. Smuggling in a few dozen troops each riding a horse and leading a large stud loaded down with enough goods to supply a small army for the better part of a year? Not so much... The quality of the besieging forces is an important factor too. A mediocre siege commander with manpower shortages will have difficulty maintaining a total blockade. The reincarnation of Alexander the Great leading a 5000 strong army? That place is airtight. Quality of defenses would be a factor too. Stronger defenses means the blockade has to be more distant and cover a larger area, making it easier to breakthrough via local local superiority, since by the time the entire army has converged the assailants could already be long gone.