Possibly a primer problem (bad batch or whatever) but FWIW I've loaded a few thousand .44 mag/.44-40 with CCI primers from about 4.2gr of Bullseye up to 18gr N110 (not in the .44-40 obviously!) and some in between with N320 and not seen this issue, so I don't think it's inherent to CCI.

I did have a batch years ago where I don't think I quite dried the cases properly after wet cleaning, but they were just going click rather than being underpowered/poor burning.

I don't think a primer by itself would get a bullet out the barrel so I'd guess you've had at least partial powder burn in all cases.

Would someone in your club swap some different primers to try?