Take up bowling, and keep the ball behind the passenger seat.
This is very common on Fox bodies, but I'm not aware of it being a problem on the 99 and newer Mustangs. At least not yet. It's usually caused by worn out springs. The drivers side will always wear faster than the drivers side for the simple reason that there is always a driver in the car when it's being driven, but there isn't always a passenger.
Take care,
ÅChris