The biggest difference between mechanical hard disks and mechanical watches is the fact that watches are fairly low-tech. One person and the right tools can grind gears, make springs, pretty much do the whole operation. The raw materials for this have many other uses, and will always be readily available. Any person investing time and a few thousand dollars in tools can make mechanical watches just for the sheer love of it. Incidentally, with clocks being in every electronic gadget these days, watches in general are dying out. I never wear one any more, and I don't even carry a cell phone. It's easy enough to find a clock somewhere, assuming I don't have my GPS on me which I usually do. Truth is the rare times I go out for fun, I couldn't care less about the time anyway.
Mechanical hard disks on the other hand require expensive, sophisticated machinery to make. They also require a clean room. Once they are no longer economically viable ( presumably because SSD hit the same cost per GB ), there will be no incentive for a profit-driven company to make them. And there will be no way an individual who is in love with the technology to make them either ( unless that person is a multimillionaire ). So yes, once they're gone, they're gone. I can even see small runs of incandescent lamps being made for die-hards who refuse to use LED eventually more than I can see hard disks being made. Most people only care that their data is reliably and cost-effectively stored. The technology used is irrelevant.
