I'm not sure the two are really comparable, though.
If an actor dries or gets lost, okay: someone on stage eventually has to say something, and through improvisation or sheer force of personality, the show will get rolling again. If your cast is really really good, the audience won't even notice the lull.
With music and dance, if the company gets lost, you're in serious trouble. The audience will notice. Confused dancers are by-definition a safety hazard. (Things which would be mere mistakes in dance rehearsals can now become catastrophes. If you miss your mark, you fall off the stage. If you go out of sync, you start colliding with other dancers. If you realize you're in the wrong place and rush to where you ought to be, you collide with set and props. etc. etc. etc.) Singers can easily pick up their place if they get lost, but instrumentalists have a much tougher time, particularly in smaller pit bands. I've only ever known a few musicians who are capable of bootstrapping themselves seamlessly into a running number. (Of course, if your musicians are a rock combo, that becomes much much easier than if you have a more traditional score--but in that case you almost certainly wouldn't have a conductor.)
You don't stop a number every time the second bassoonist blows a pick-up note, but if the conductor has well and truly lost her place in the score and control over her musicians, it starts to become a good idea.
(And, to cover my ass, I don't mean to suggest that dancers are especially stupid or ignorant or incapable of handling themselves. The job they do is quite risky even when conditions are absolutely perfect, and any amount of confusion can become a very big problem very very quickly. In all but a few circumstances, even if an actor completely drops the ball, nobody gets hurt, nothing gets damaged, and we keep on going. In all but a few circumstance, if a dancer is even slightly off, you start running a very serious risk.)