I've got a fiver on this one ...

 

and ive got a fiver that says he had no leak - he parks outside and its been getting progressively colder

 

The pump is broken or does not have enough power to inflate a completely flat tire.

I bought two tire pumps one at an Auto store and the other at Sears.

Neither portable pump would inflate a flate tire. So much for those items. They're only good for a low tire.

Try a real compressor. If I remember correctly I had two people tell me the samething happens when they buy a compressot tank that holds air. Not enough force to fix a flat.

Try the real thing, I bet it works.

Edit:
Posted this before I read you took it to a tire store. But the above is still good facts to know.

 

Oh, i just remembered........

The bead may be broken and not sealing. You should know this or at least a good tire store should know that.
They need to use soapy water to see the air leak. Many mechanics are deaf and can't hear the air leak.

I've had problem and even the tire mounters have had problem getting a tire to reseal at the beads. Sometimes they have to completely brake it down three times to get the bead to seal up.