The original post got my attention, with its subject line, as my first fulltime job in radio was at WKNY in the mid 60's (the year, not my age). Since the poster asked what "could" cause the described phenomenon, I'd theorize that close-in cancellation of groundwave by skywave is occuring, even though Kingston and Poughkeepsie are only about 15 air miles apart. Further, even though the effect was described as apparently not sunrise or sunset related, the pattern is close enough to be generally characterized as daytime-nighttime occurences. The raising and lowering of the reflective layers of the upper atmosphere are not typically in strict synchronization with the local sun times which are more closely related to the seasonal tilt of the earth on its axis. The medium wave AM broadcast band is particularly subject to this effect, and there doesn't have to be a whole lot of power involved to experience the phenomenon.
With regard to the side-thoughts of this thread, about the efficacy of the fulltime Class IV regionals, most (if not all) found that the "in-town" coverage at night was considerably improved at 1 kW, with its greater ability to overcome the electrical, man-made noise, etc., but that the "fringe" coverage at night was very much less than it was even at 250 Watts, by virtue of the increased interference levels encountered. The NAB got what wanted but it very much wasn't the relief the owners anticipated, especially vis-a-vis the new electric bill.