Here's a breakdown of why:
* Relay Failure: The antenna motor is controlled by a relay. This relay acts like a switch, energizing the motor only when the radio is turned on and the antenna needs to extend or retract. A stuck-closed relay will keep power flowing to the motor even with the ignition off.
* Short Circuit: A short circuit in the wiring harness leading to the antenna motor could provide a constant power source, bypassing the normal on/off control of the relay. This could be due to damaged wiring, a corroded connection, or a short within the motor itself.
* Faulty Antenna Motor: Although less likely given the low mileage, a faulty antenna motor could be drawing power even when it's not receiving a signal to operate. The motor's internal components might be shorted.
* Improper Ground: A poor ground connection can cause unpredictable electrical behavior, including malfunctioning of the antenna system.
Troubleshooting Steps (in order of increasing complexity):
1. Check the fuse: Although less likely to cause *continuous* operation, a blown fuse *could* be preventing the antenna from retracting, leaving the motor running. Locate the antenna fuse in your fuse box and check if it's blown.
2. Locate and inspect the antenna relay: Find the relay for the antenna motor (your owner's manual or online forums might be helpful). With the car off, try gently tapping the relay to see if it disengages. If it's sticking, it needs replacement.
3. Check the wiring harness: Visually inspect the wiring harness connecting the antenna motor to the radio and relay. Look for any signs of damage, chafing, or corrosion. Pay close attention to connectors.
4. Test for power at the motor: With the car off, use a multimeter to check for power at the antenna motor's wires. If there's continuous power, you've confirmed a short circuit somewhere upstream.
5. Disconnecting the Antenna Motor (temporary): As a quick test to confirm if the motor itself is the problem, *carefully* disconnect the electrical connector to the antenna motor. If the continuous running stops, the motor is the culprit.
Important Considerations:
* Safety: Work on the electrical system with the car's ignition off and the negative battery terminal disconnected.
* Professional Help: If you're not comfortable working with automotive electrical systems, it's best to take your car to a qualified mechanic. Improper repairs can lead to further damage or even fire hazards.
The low mileage suggests this might be a simple relay or wiring issue rather than a major component failure. Starting with the simpler troubleshooting steps is recommended.