Check the wiring at both ends. It is possible that the connection to the camera of the connection to the reverse light circuit is either loose or broken. Also, double check your camera/monitor ground connections. A bad connection can cause problems such as you are experiencing.
If the camera is a wireless model it is possible that there is interference from another device which is on the same frequency. This can come from wi-Fi signals or bluetooth devices, home security systems, cordless phones, and even microwaves. You may have to move your RV to a vacant area -- away for possible signal interference -- to confirm that the problem is not a signal issue (if using a wireless camera).
Keep checking, and you'll find the answer.