I had the same problem with my Raspberry zero. The RPi zero case is very tight and difficult to install the camera.
The problem is with the camera itself, not the cable that goes to the RPi.
What happens is that the camera sensor has a connector to the PCB that can become lose, so when I was trying to attach it to the case this cable was unhooking from the PCB. Every time I tried to push the camera to attach it to the case this cable was disconnected.
I solved my problem by adding a piece of folded paper between the case and the connector acting as a spacer just to keep extra pressure while I was inserting the camera fixture in the slot. It was tricky but it worked.
Hopefully this will be helpful to others