Typically, rope lasts forever.
There are no rules about ropes breaking on use, unless they are explicitly broken/cut.
A rope is usually reusable, unless of course, you cut it to length. Though if you think about it, this can almost always be avoided, and the only reason you typically need to do this is if you
- need two lengths of rope at the same time
- will leave part of the rope behind, like when descending into a chasm and you can't (or don't want to) untie the rope you fastened to that tree up there
Look at the most common uses for rope:
- Binding: You can just coil 50ft. of rope around your prisoner's torso (Or whatever length of rope remains after binding his feet and hands (no reason to cut here, too). It's only 10-15 coils. He might not like it, but if you cared, why would you bind that person?
- Climbing: Trailing rope never hurt anyone
- Rigging: Isn't getting caught in a coil of rope even a trope of some sort?
In D&D 3.X/Pathfinder, a silk rope costs 10gp, which is a "non-issue" from level 3 onwards, at the latest (assuming somehow normal wealth). It also has limited weight, carrying around multiple ropes in a Handy Haversack or Bag of Holding is very simple. Even without that, you will usually not suddenly need more than 50ft. of rope per character.
At this point, keeping track of whether or not you break or not break your rope is not only tedious, but also pretty pointless, since the "danger" is usually no problem at all (spare ropes, see above).
Of course, there may be games where having a rope is a huge advantage, such as survival scenarios. In these cases, narrative rope-breaking may be beneficial to the story and is usually fair game.