Are Saturn's rings stable?
Most of Saturn's rings are inside it's Roche limit, which means they will never clump together.   Tidal forces prevent this from happening.

small objects that are already together can withstand the tidal forces.    A sufficiently large body inside a planet's Roche limit should break apart by tidal forces.   That may be how the rings formed in the first place, or they may have formed by collision.

Saturn's rings are thought to be relatively young, if 100 million years qualifies as young, but it is for objects inside the solar system.    Being young doesn't tell us how long they will last.   I think the 300 million year estimate may be accurate enough, originally mentioned in the comments, but until that happens, the rings will remain, just grow smaller over time and they'll never coalesce into moons.  

As a footnote, Saturn's thinner outer rings or gossamer rings are outside the Roche limit, and those might, one day, form into moons, or they may be too thin for that to happen.  A certain density is probably required for moon formation.