Do you have Goat Heads?
They're just nasty.
I'm not sure if there is any single solution to them. Certainly picking them out of the tires every once in a while helps. Get the stickers out too. If you've gotten several flats in a week, it is possible you missed some thorns.
There are a couple of solutions that people have tried. One option is to use tires with a thick absorption layer, so it is less likely a thorn will stick all the way into the tire.
Schwalbe Marathon Plus
Michelin Protek Cross Max
Tire liners may also help.