I was having the same problem. Never resolved it with the Morrell target I was using which pulled off the field points. They would come out easily and catch on the woven fabric covering the target.

The field points are larger in diameter than the arrow shaft. I tried regluing new points but it never worked.

Finally since I live on a ranch, I just got two hay bales and used a strap tightener to cinch them up as solid as possible. Never lost another field point.