I was getting too many flats on my old Schwinn World Tourist. It was very frustrating as they kept on coming even after switching to Kevlar-ply tires. I then went to plan "B" which was to eliminate all rough areas on the inside of the wheel rim (via dremel tool), replace the plastic rim tape with cloth rim tape, and add a liner between the tube and tire. I only have had 1 flat in roughly a year after going to plan B.

If you or the bike shop didn't find an object in your tire the caused the flat, thenI recommend replacing the rim tape first before going with the high dollar tires.