The truth is, it is relatively difficult for an animal to escape a trap. If traps didn't work more or less reliably, folks would not continue to use them. But this is predicated by the animal having its foot in the trap. Deer are the exception. They have a hard tapered foot, and they can pull out of a trap in a second.
Sometimes a animal, especially a canine, might roll on a trap and fire it. I've also had canines spring a trap by sliding into a dirthole on their forelegs. (But that is rare.) Other animals may at times lay on their belly at a set and fire a trap, again a rare occurrence.
Endeavor to persevere.