Yes, good point that I hadn’t thought of, thanks. It’s very easy to imagine far-future technology in one respect and forget about it entirely in another.
To rescue my scenario a little, there’ll be an energy cost in transporting the iron together; the cheapest way is to move it very slowly. So maybe there’ll be paperclips left for a period of time between the first pass of the harvesters and the matter ending up at the local black hole harvester.
Empirically we seem to be converging on the idea that the expansion of the universe continues forever (see Wikipedia for a summary of the possibilities), but it’s not totally slam-dunk yet. If there is a Big Crunch, then that puts a hard limit on the time available.
If—as we currently believe—that doesn’t happen, then the universe will cool over time, until it gets too cold (=too short of negentropy) to sustain any given process. A superintelligence would obviously see this coming, and have plenty of time to prepare—we’re talking hundreds of trillions of years before star formation ceases. It might be able to switch to lower-power processes to continue in attenuated form, but eventually it’ll run out.
This is, of course, assuming our view of physics is basically right and there aren’t any exotic possibilities like punching a hole through to a new, younger universe.