Understanding the occurrence of Earth-sized planets in the habitable zone of Sun-like stars is essential to the search for Earth analogs. Yet a lack of reliable Kepler detections for such planets has forced many estimates to be derived from the close-in (2 < P-orb < 100 days) population, whose radii may have evolved differently under the effect of atmospheric mass-loss mechanisms. In this work, we compute the intrinsic occurrence rates of close-in super-Earths (similar to 1-2 R-circle plus and sub-Neptunes (similar to 2-3.5 R-circle plus) for FGK stars (0.56-1.63 M-circle dot) as a function of orbital period and find evidence of two regimes: where super-Earths are more abundant at short orbital periods, and where sub-Neptunes are more abundant at longer orbital periods. We fit a parametric model in five equally populated stellar mass bins and find that the orbital period of transition between these two regimes scales with stellar mass, like P-trans proportional to M-*(1.7 +/- 0.2). Ptrans These results suggest a population of former sub-Neptunes contaminating the population of gigayear-old close-in super-Earths, indicative of a population shaped by atmospheric loss. Using our model to constrain the long-period population of intrinsically rocky planets, we estimate an occurrence rate of Gamma(circle plus) = 15(-4)(+6)% for Earth-sized habitable zone planets, and predict that sub-Neptunes may be similar to twice as common as super-Earths in the habitable zone (when normalized over the natural log-orbital period and radius range used). Finally, we discuss our results in the context of future missions searching for habitable zone planets.