Is an endless siege a possibility?

https://preview.redd.it/b5pz6aiw6f0g1.jpg?width=1501&format=pjpg&auto=webp&s=ced138e1bbcab7a8ef326e2d1d895775d42d7ed8

I'm on my 2000th day on the siege (I guess it happens when you lay siege Constantinapole with levies), and it feels like the Chance of Falling value won't move anymore. The Siege Accumulation says it's maxed out and things won't change anymore until the defenders surrender. Will they ever surrender? My War Exhaustion is just increaasing fast at this point and I don't want to peace us if I should just hold on a bit more.