Wow, that is weird. I have never had a python not suffocate the prey. My first python Ragnarok, was very strong and I fed her live all her life, so she got lots of constriction exercise. It is pretty graphic, but she would crush the hell out of even large prey, and sometimes blood would come out of their mouth!
With more experience, I would think the python will get better at killing. the best course is just to switch to thawing out frozen rats or feeding pre-killed prey.
Since you are feeding live, Stick with rat fuzzies for a few feedings, and once she has gotten the hang of it and put on some weight, then switch to rat pups.