Do you see "drag marks" on the fired primers, or not? If not, it may be your shells, not the gun.
Are you using cheap steel-head loads? Try a box of brass-head Winchester AA or Remington STS shells. I have several doubles that will "stick" from 50% to 100% of the time with the cheapo stuff. They shoot AA shells all day. The cheapo steel heads expand enought to prevent extration. If the extractor won't lift, the gun is almost impossible to open. Note that some cheap loads have brass-plated steel heads.
A gunsmith may be able to clean up the chambers enough to allow use of cheapo ammo, either by polishing the chamber or cutting it slightly larger at the breech end.
If you do see drag marks, the pins are sticking.
It may be a cleaning issue. There may be a buildup of crud that is causing the firing pins to stick in the forward position. Remove the stock, and thoroughly clean the action, especially around the firing pins. Penetrating oil and brake cleaner can fush out the grunge from hard to reach spaces.
The return springs may be worn. They can be replaced.
The firing pins or the breechface may have gone soft. (or the pin collets if it has them.) They can be re-hardend with Casenite, but this is not a trivial fix. (Unless you have done parts hardening before. Then it is just work.) Replacement parts may, or may not, be available.
Start with the AA shells. Wal-mart usually has them for ~$7.50 a box. Try Light Target (2-3/4" 2-3/4 dram birdshot).
