Tire service guys hate fix a flat- it must make their job tougher.
I'd look for a nail first, then at the stem second; loosen then tighten the valve, grab the stem itself and see if you can turn it a little bit as corrosion can and will form in the wheel's stem hole.
Last time I bought new tires several of the dang things had slow leaks and bringing them back to have the beads cleaned (tires and wheels) and carefully installed with bead goop didn't help. It was then that I noticed if I pushed the tire stems to one side, air hissed out. Turns out, a few years ago, a boatload of defective stems came over here from China and I got some of 'em.
New stems = problem solved in that case.
I refinished a bunch of alloy wheels last summer and took special care to sand the bead areas smooth and get down into the stem hole with a dremel to remove corrosion and warts from that too. Then I took special care to prime and paint the beads and stem holes; then on top of that I waxed the **** outta them, as well as the rest of the wheel. I am hoping to see an improvement in corrosion resistance from all that.