The rings are rather close to Saturn and the differential gravitational fields are big enough to tear medium sized bodies held together only by their own gravity apart. this is sometimed called the Roche limit there are some very small bodies in the rings called shepherd moons that are presumably continually accreting and losing material
Other planets have rings too. Uranus has some that were discovered in a flyby, and didn't I read somewhere that our very own Earth has a faint ring? It's a stable gravitational solution; why should it condense?
In fact, rings come from moons broken apart by tidal forces. The process does not work the other way. When a moon gets too close to its parent body, it can be torn apart by the gravitational forces, eventually forming a ring. The individual particles gradually lose orbital energy through collisions and eventually fall down to the planet. Astronomers speculate that rings last about 50,000 years.