Why have sieges in warfare from ancient times through the medieval era (and later) consistently lasted months or even years, and what sudden events or circumstances typically allowed them to finally break through?

Many historical conflicts feature a surge, where enemy forces surround a city or fortress and try to break inside.

As the title mentions, from ancient times to now, these consistently seem to take months to years in some cases.

What factors would allow this prolonged siege to suddenly end, and how come they consistently have taken this long? What factors would allow them to finally get in?