Considering the overwhelming success Ruger has had selling .375 Ruger chambered rifles, I don't expect it to disappear any time soon. The H&H isn't going anywhere either, but I expect that rifles chambered in .375 Ruger will be outselling rifles chambered in .375 H&H within a decade, if it's not happening already.
Hornady has had some trouble keeping up with the production of brass and ammo since the cartridge has proved to be so popular. This is a great indication that it's longevity is virtually guaranteed. They seem to have caught up, as ammo and brass is much more widely available now than it was 2 or 3 years ago.