Hi climber1,
I ran into the same issue with my bike. I'd patch or replace a tube and the next day I'd have a flat tire again. Happened more times than I care to admit. I checked the tire for goat head thorns but usually wouldn't find much.
Finally, I took the bike to a local bike shop in town and asked what was going on. Found out that I wasn't looking at the tire close enough. I needed to take the tire off the rim and look it over carefully. After close inspection, I found that the tire had pieces of glass, thorns, and staples lodged in the rubber!
The procedure that's worked for me:
- find a point on the tire that's easily identifiable (logo on the side is what i usually use)
- holding the tire with both hands, start to rotate it slowly beginning at the identifiable point
- when you find a cut or abrasion in the tire, pinch it to increase the size of the cut
- if there is any debris (glass, metal, thorns) in the cut, remove it with a pair of needle nose pliers, tweezers, or fingers
- keep rotating the tire until you've reached the point you identified
- once you're done, put a new tube in the tire and remount it on the rim
By doing the above, I haven't had a flat in a long time. I can ride my bike instead of fixing flats all the time!
Good luck!