TWiV had Daniel Griffin on again for a clinical update. They discussed two of his cases with potential reinfection. It may also have been the same infection the whole time, it just went dormant/below detectable levels for a couple of months before coming roaring back. Wouldn't be able to tell for sure without being able to genetically sample the original March/April samples and the July samples from the same person. Not great either way, though.
https://www.microbe.tv/twiv/twiv-638/
However, my understanding is that vaccine-induced protective immunity (the kind that prevents you from getting sick in the first place) can be completely different from natural viral infection-induced responses. So even if the natural immunity is relatively short-lived, a vaccine could still very well work with a completely different biological mechanism and be longer-lasting.
But, yeah, it's still a possibility that natural immunity doesn't prevent reinfection at a later date. Plenty of real-world viruses to look at for examples. Or it could never go away completely. Some of those, too (think HIV).
This is from the EU's CDC equivalent:
https://www.ecdc.europa.eu/en/covid-19/latest-evidence/immune-responses
The short answer on a whole lot of COVID, especially medium- and long-term stuff, is "we don't know; it hasn't been long enough to know." But this has gotta be the largest collective medical/research endeavor in human history. So many medical labs around the globe stopped all research except COVID-19. The experts and researchers remain pretty optimistic that there will be some sort of vaccine, hopefully within a year.