You have not provided enough information for a reliable long-distance diagnosis, but I suspect that the cases have been reloaded too often and the case neck has stretched. Have you checked the case length? When you insert an empty, resized case, the mouth of the overlong-neck is right up hard against the tiny step in the chamber where the transition a.k.a. throat starts. This step will have a slightly bevelled edge, so the case mouth can be forced in if it is a couple of .001! too long, and you will not even notice that the mouth has been "resized" by the bevelled edge of the transition step. This works because the freshly sized empty case is undersized, compared with the loaded diameter, to provide grip on the bullet when it is loaded.
When you now seat a bullet in that overlong neck, the mouth diameter is expanded by the bullet. The mouth cannot now be forced into the transition step, being held wide by the bullet, so the case jams and cannot be chambered.
On the cases which you did manage to fire, the mouth has now expanded to fill the bore. And the neck has lengthened again, now being tight up to the step, but the case is being held in lengthwise compression by the bolt. When you extract this case and it is able to spring back, you find that it will not chamber again.
Take one of the problem cases. Fired, but NOT resized. Ink over the case neck and mouth with a felt tip pen. Allow to dry for several seconds and then try to chamber this case. Repeat several times. Take out the case and inspect the end of the neck and the case mouth under a watchmakers eyeglass. If you see scuff marks on the case mouth, then the diagnosis is as described above - the cases are too long ...measure them!
I may be wrong, but if I am right, you are heading for a serious case-neck separation with a neck jammed up at the transition step - which can be a PITA to remove, and I described such a problem recently (with photos!). Those cases are past the end of their useful life!
Someone may suggest that you trim the cases back to a correct overall length again. I would advise against that false saving, which may cost you considerably more in FUBARed rifle than any cases are worth. Non-US military chambers are typically somewhat looser than SAAMI-standard brass, so if the case has become so long that it is jamming, then the brass has been seriously overstretched!
Bin the problem brass NOW and get some new cases. Not range pickups with an unknown history!!!