Is the fired case getting stuck in the chamber? If so you need to give the chamber area a good scrubbing with a bore brush and inspect it to see if there is any roughness in the chamber from rust or poor machineing.
Could be it's had 44 specials fired that left a ring of carbon at the end of the case mouth and the longer 44 mag hull is hanging up on it.
Theres a recess in the breach end of the barrel for the extractor to fit into. If theres crud in there it can prevent the extractor from snapping over the rim. There could also be crap under the extractor itself keeping it from engaging the rim good.
Those are the things I'd look at first.