It happens with video and not music mostly because video content is spread across more companies than music. Also, Apple's such a big part of the music business now that the only way to hurt them would be for everyone to drop them, and the only way for that to be at all feasible would be for them to conspire, which would be collusion, which is illegal.
As for video rights, the content owners saw what happened to music with iTunes and have thus been a lot more reluctant to hand the power over to one entity like Netflix. The deals they make only last so long, and if they can't come to an agreement they get dropped. You see this less on Amazon Prime because 1. Amazon's trying to buy their way into this market and are throwing their weight around to make deals, and 2. the content companies are trying to make Amazon into a true competitor to Netflix, which would give them more leverage in these negotiations with both of them.