Pumping up the tube to twice its diameter is a good idea to locate punctures as it also stretches the hole and makes locating it a lot easier. However the 2 or 3 psi involved may not be enough to effectively test the valve for a leak.

I recently had such a problem so tested with tyre and tube mounted and pumped up to 80 psi. I immersed the part of the rim with the valve in water and sure enough there was air escaping from the valve. At 27 psi this stopped - which I guess is why my tyre would go soft but not flat when left for a few days.

Cheers, Adrian