Quickie tech talk for the uninhibited,
Many car stereo receivers uses two antennas for something called diversity reception or multipath reception. What that means that that two antennas receives the signal through multiple paths. You can think of it like echo receptions on two antennas.
With only one antenna working, you could be feeding a weak signal to the radio and the station would drop out due to signal/noise ratios. Some radios have better S/N ratios and can overcome this weakness. In yet some better cases, one antenna would cause radio stations to come in and out, called fading.
Assuming that the receiver's tuner section is not bad then you are likely running off just one antenna. In the '01, you have the rear window antenna with a terminal plugged into it that feeds to one side in the back of the receiver. And you have a separate antenna amplifier, instead of a power antenna, which is located in the inside the passenger side rear pillar, and that feeds another section of the receiver. This wire feeds through the passenger side headliner up to the rear of the receiver.
What I would probably have done in you case is remove the receiver and connect a separate wire to one of the two antenna inputs. If the reception improves then troubleshoot that antenna section. If it still doesn't work, then try the same trick on the other antenna. If neither work then you probably have a problem in the receiver.