A couple of questions. Are you sure you are hearing static from the radio? The backup camera has a microphone. Normally you will want to hear this when vehicle is in reverse (to hear directions from spotter when backing up) . It is possible this is set to have audio on at all times. If so, you may want to change setup to "reverse only ".
Assuming that is not the issue, what are you listening to on the radio when the problem occurs? Some signals (like AM radio) are susceptible to interference more than others.
2012 Forest River Sunseeker 2300 Chevy