Last night I spent the midnight oil trying to find out what was causing this to my iPhone 6 and now to my iPhone X, the culprit is iTunes, every time that I was syncing my phone with iTunes for some reason and after it synced, when I wanted to start an app, the phone asked me to enter the password to my iTunes account, and that had to be done for every app that I wanted to start. To solve that, I was using the solution which I explained in my previous post, that worked only until I have to sync again.
Final solution:
I started iTunes then I checked to see if I was logged into my account, and to my surprise I was not. So I login into my account and then authorized my MacBook Pro, then I synced to see if that was the problem, to my surprise that was it, that fixed the problem.
In this case, there was nothing wrong with iTunes, but my own ignorance of not knowing how to use this software. I synced many times just to make sure and everything is working as it supposed to be. But thanks to your post I took those extra steps to find the culprit of this issue.
I hope this solution apply to your problem.