You can determine the source of the leak by filling the tire to the normal pressure and applying soapy water with a spray bottle or even an ordinary paint brush. The soap will not damage the tire or rim and when applied to an area that is leaking air, will bubble up to show the region of the leak.
Your tire valve can leak at the rim edge, but also can leak internally at the valve mechanism. If your rim is damaged but not easily seen, the bubbles will grow at that portion of the wheel.
Do not discount either the possibility of a "filled puncture" in the tread area. Apply the soapy water to all of the tire and wheel to ensure you don't miss a section.
You can inflate beyond recommended pressure to have even more force behind the leak, but remember to return the air pressure to normal when the testing is completed. I was unable to locate a safety factor regarding over-inflation, although I have in the past inflated a 45 psi tire to about 60 with little problems or danger.