Call_me_jorge said: "Do associate directors have to be at every performance? Don't some asociate directors have to oversee every production of the show?Also do the original directors still get paid after they step away from the production?"
Associate directors who remain with the show and are integral to maintaining it, taking a lot of that responsibility from the PSM, are becoming more and more common, to the point where SDC was negotiating to have health and pension payments included in their new contract with the Broadway League earlier this summer (Disney already has this in place, so the associates on The Lion King and Aladdin are already covered). So depending on how the artistic team is set up they may indeed be there every night.
The director and choreographer will continue to receive royalty payments each week the show is running.
And nasty_khakis is absolutely correct. I have been in long-run situations where there are certain things you just end up not being able to correct as the PSM, or even an associate. Not necessarily things that are terrible, but sometimes things are just a little too big, or too subtle, and it takes the cast knowing that the director is going to be popping in to bring them back in line. Or sometimes it's even just a case of wanting to let the director see how the show has grown. I encourage the directors who want to check in to keep it on the down low, as the cast will often go into "best behavior" mode if they know the director is coming in, and then you sometimes lose moments that have developed during the run, both good and bad, because they are trying to focus on what they think the director wants to see, as opposed to what is actually happening each night.