The best way to avoid punctures is to be very careful in areas where there are thorns. And, only use your pad in the tent or on a ground sheet, never directly on the ground.

A gal I used to work with was telling me that her boyfriend got a puncture, bought a second new air mattress and punctured that in exactly the same spot. They found a thorn in the tent floor.

I discovered part way through my last tour that self adhesive inner tube patches work well on air mattresses.