The only Handis I've known to shoot loose are those that have been reported here, all but one(JPH45's in 1300 rounds) were relatively new rifles and probably were attributed to burrs on the underlug and or sloppy fitting by H&R to begin with. To my recollection they were all fixed by H&R and promptly returned to the owners. I haven't had any of mine loosen up, but I probably haven't shot mine enough for that to happen, either. For the amount of shooting the majority of shooters do with the high pressure calibers, I doubt it very much that it will be a problem, and if it does happen, H&R is there to fix it if need be, they back their product very well, even after the normal warranty period. JPH's shooting habits, shooting every day and putting 8000 rounds thru 4 Handis in 3 yrs is a lot of shooting by anyone's standards!!
FWIW, I have close to 100 rounds thu my .338-06 Ultra, it's still just as tight as it was when factory fitted, it locks up tight on a .001" blade, tight enough that the blade can't be pulled out, which is as tight as any can be IMO. Those rounds are on top of the 200+ rounds that went thru it as a .25-06 before I got it as I bought it used.
My SS '06 Handi has what appears to be a stainless hinge pin, the underlug appears to be stainless as well, the barrel and underlug don't have the appearance of the frame, but since I'm not a metalurgist, I have no idea how much nickel is in the barrel and underlug. Maybe someone can offer an opinion on the wear characteristics of stainless as applicable to your question.
As Fred stated, his shooting loose was due to the epoxy work that he used to reinforce/fit the underlug to the barrel. Matt Parliament used epoxy to fit a barrel, maybe he'll check in about how that's holding up. I've only done one .270 barrel and didn't shoot it much to really test it, but it did shoot fine with factory ammo.
Tim