Is your idling stable over Petrol?
Which Plugs are you using?
If you have an after-market CNG, then there will be a venturi at the end of the pipe which connects the CNG kit to cumbustion chamber. But if you car has no issues of loss in pick/acceleration then that should be fine also.
Which engine oil are you using? do check its level with the dip stick, it should be in between the two marks over that stick.
If all above things seems fine, try adjusting the idling screw of the CNG kit over a hot car, lower it down to the full clockwise till the engine shuts down, then turn it anti-clockwise slowly till you feel that the engine has regained its required RPMs. RPMs should be in between 800-1000 over idling and engine should be running smoothly over that.
Let me know if that helps, if still not I feel its a valve related issue. If they are jammed, over petrol the car somehow manages to perform but over CNG (which has less power) it gives lower RPMs and can not maintain the engine.
But dont let anyone mess with the Head and Valves untill you are pretty sure that the problem is not due to anyother thing,