The problem is Wind Magic mentioned "I ride on gravel roads for the most part" which rules out road bikes. I used to ride my mountain bike on trails, gravel roads as well as single track and never had a flat over many years so I too wonder if there's a problem with the wheels or spokes. I expect the knobby tires I formerly used also afforded some flat protection.
I do a lot of cycling over the summer, all on roads now. I haven't seen the tires you use but I've been very pleased with the Continental Duraskin (Ultra Gatorskin) tires (with Flat Protection System) I found several years ago. No punctures (touch wood) and tremendous wear. Wind Magic, if you can't find the ones mentioned by John, try looking for the Continental Tires I've linked to below. The web description mentions flat protection.
John - the above link is the tire I use. BTW - do you follow road cycling closely?