Here are my thoughts on how the system works, though I'm only guessing:
- When you press the button on the keyfob, it transmits a signal to the car. The car is always listening for this signal, so it can respond immediately.
- When the keyfob is in standby, it just listens for a signal from the car, to which it replies by transmitting a signal back to the car. (Since transmitting uses more power, this work is left up to the car.) The car sends a signal a couple times per second, and when the keyfob replies, the car responds by turning on lights, allowing the door to open, etc.
Maybe the car isn't transmitting its signal a couple times per second. Since the problem only occurs on the driver's side, it sounds like it might be a disconnected or broken antenna on that side. I believe there is a separate antenna at each of the three door locks.
(Of course, it might just be interference. Thing is, it's an RF device (not sure which, but all consumer frequencies are pretty crowded), and many things can interfere with the signal. Maybe try backing in to your driveway, so your doors are switched.)