Drifted or punched makes no difference unless the stress is enough to physically tear the ring. It doesn't have any effect on rivets coming out - that's all from rivets not properly set / tightened. The way you'd see substantial difference in them is in actual combat where the rings are getting strained / stretched. Normal wearing should have minimal strain on the rivet itself; the ring bears most of the weight and is distributed across the whole row of rings, so strain on a single rivet is trivial - again, unless it's not set well, and the mail moves in a way that adds stress on that ring. But drift or punch isn't much concern for around the house / faire usage.
Historical mail is a mix and match of flat or round wire. I haven't seen any that was cone shaped rings with a flat backside, though. Either flat on both sides, or rounded. There's a whole lot of things that separate the mail we have from historical mail, not just shape or riveting. Historical mail sometimes had rings of different sizes on the same piece. And rings of differing thickness on the same piece, much like historical plate had thicker and thinner spots. Even outside of us having completely different material, there are plenty of things "wrong" with what we have for mail. Still a lot better than the butted stuff from a decade ago though!
I haven't seen any mail for sale that is wedge riveted, alternating rounded solid rings, with rounded rings. The closest is wedge riveted, alternating flat round rings, and flat rings. Wedge / solid / round would be pretty awesome, though.
Count up how many rivets you've lost, vs how many hours you've worn the hauberk, and talk to Icefalcon. No promises he can do anything, but he could probably tell you if it sounds like a bad batch or bad luck.
