Mr. Francis Jackson, Operations Director in Alton Towers Resort, UK, gives a very interesting explanation of why sometimes Theme park rides stop, showing us the backstage of his park. Very important video to be seen by everybody.
Summary: Mr. Francis says that the most common causes for a ride in a park to stop are:
1) Public using cameras or cell phones to take selfies or to film the ride; This could be very dangerous for self and for others, so if the operator sees something like this, it must stop the carousel.
2) Public who sometimes feels sick during the ride; As the operator realizes this, he has to stop the ride for passenger's welfare.
3) Personal belongings falling on the ground; Since we need to retrieve these objects, operators must stop the ride to do so.
4) Extreme atmospheric conditions such as snow, ice, strong winds and rains sometimes oblige to close the carousel.