I too have the exact same problem, i took the iphone 6s to apple store and they replaced the phone for me ( phone was ust two weeks old ) and while I was waiting for my other iphone screen to be changed, the replaced phone also gave the exact problem where the menu disappears and comes back after couple of operations.
This is what I can assume the problem is.
1. purely a bug which apple needs to fix , 9.3.2 and 9.3.3 gives me the same problem
2. could be a profile or apple id issue
Hopefully apple fixes this soon as its a little annoying
Tried all the above steps with no success. Even a phone replacement did not help in my case.