It sounds like there might be a short in the wiring. Have you ever hit your controller or thrown it. Try taking the back off and taking a look at the wiring for the vibrator. You may even have to replace the vibrator. DualShock 3 Vibration Motors Replacement If the motors are fine. You might just want to get a new motherboard. DualShock 3 Motherboard Replacement Or get a new controller.
I had this problem before but its not something I can explain online so easily. If you have the 80 some dollars to spend on the repair follow this link... https://rma.scea.com/rma/rma.htm?_flowEx...-8FA8-4664-30AA-A9FF6B176685_k79B5721A-C1F6-FF7F-CD93-78EF4D85E185#