The Witch-king's occupation of Fornost only lasted for a year, after which he was expelled by the forces of Gondor. Nonetheless, the Northern Dúnedain seem to have made no attempt to reoccupy their old capital. Perhaps their numbers were too few after the desperate fighting of the preceding years, or perhaps the Witch-king left too great a residue of evil behind him in the city.
Whatever the reason, Fornost fell into desolation and decay over the next thousand years, and was a mere crumbling ruin at the end of the Third Age. After the War of the Ring, Gandalf predicted that Aragorn would come north and rebuild the city, but it's unclear exactly when this refounding of Fornost took place.