It sounds like it may be a heat issue. If it will fire the first three rounds when cold but then start sticking when it heats up a little, take a look at:
1....Varnish build up in the chamber. A lot of 7.62x39 ammo is painted with varnish. When it get's really hot, that varnish can melt onto the chamber and stick there. Then later, when it gets warm, it gets sticky like honey. Use a hone to polish the chamber.
2....Mis-aligned piston and/or tube. There may be enough clearance when it's cold but as it heats up, clearances change.
3....Built up crud inside the mechanism.
Give it a good disassembled cleaning, check #1 and #2 and post the results. Keep yer powder dry, Mac.
Tuff-Gun Finishes. The Name Says It All.
Mac's Shootin' Irons