When a system constantly restarts/resets itself, it's always something hardware, The problem is what?
Power, ground, short
Incorrect installation
Bent PINS in CPU socket
Incompatible memory
or Incompatible other hardware
This is why I would recommend bench testing.
While motherboards are made pretty sturdy, I suppose you could break or damage one if you flexed it very hard.
This shouldn't happed if you are using standoffs in the corners and middle of the board when mounting. If the system shuts off when the board is flexed, I would ensure it wasn't grounding to the case. You should not have any reason to flex the board in the first place, so once mounted securely, it should run.
You can take the board out of the case and bench test it. If it fails when flexed in your hands, its damaged. We're not there to see the behavior, but it should be fairly easy for you to diagnose.