I found this on a Winnebago owners forum, posted by Jensen customer support:
If the radio in question uses a three-wire power system (+12V DC BATT+ (constant), +12V DC Ignition/Accessory (switched) & Ground), the most likely cause for the radio to turn ON unexpectedly is that the radio is wired so that the IGN/ACC+ and the BATT+ are both wired to a constant power supply and the radio is responding to a voltage fluctuation on the electrical system.
Three-wire radios use the +12V IGN/ACC to "tell" it when to turn ON or OFF, just as a dash radio responds to the ignition when you turn the key ON/OFF.
If the radio is wired so that the IGN/ACC+ and the BATT+ are both wired to a constant power supply, the radio will remain ON at all times. With this type of installation, when you use the POWER button on the radio or remote, the radio will enter a standby state. This will allow the radio to "monitor" the buttons for user input (for example, pressing the POWER button again to turn the radio ON).
When other devices create a load and draw down the voltage momentarily, the radio will turn OFF. Upon return to normal voltage, the radio will turn ON. This would be the same as cycling the key in the ignition.
If you are unable to stabilize the power system to prevent this transient voltage, the best solution would be to install a two-position switch in-line on the IGN/ACC+ wire. This switch will allow you to remove power from the IGN/ACC+ wire so that the radio can enter an OFF state, and thus will prevent the radio from turning ON until power is re-applied via the switch.
JENSEN and Voyager Tech support Team