Can a creative team member be fired after the show is open?

The Scarlet Pimpernel, which had been directed by Peter Hunt, opened to mixed to negative reviews. It then closed, was redirected by Robert Longbottom, and re-opened (to more positive, if still lukewarm reviews).

This is one of those questions for which it would be helpful to know the prompt. In general, the answers above cover the landscape. Aside from the oddball 2.0 situations, the creative work is done, and the ongoing compensation is not tethered to the maintenance function. A production could attempt to ban a director from that function and the creative could resist, but without knowing what the OP has in mind, a deeper exploration of the possible issues would be a waste of time. If there is an actual question, ask it.

I still can't understand how Randy Houston Mercer's make-up designs for Kinky Boots haven't been thrown out and redesigned. It's baffling to me.

The answer is yes. I assume that the real question being asked is whether or not the "original" would still receive residuals. There is unquestionably contractual language to address this. Whether or not anyone here knows what it is might be an entirely different question.

The term "frozen" is used mainly to address the fact that at some point they have to stop tinkering with the show, but shows are never carved in stone. The longer they run, the more likely they will experience changes (save for Chicago, almost every single long running show has had modifications of some kind since originally opening).

Are they still using his work/designs? Yes, they are still paying him. They have a contract and are legally bound to it. Do they ever have to hire him again? No.