Hot Jupiters orbiting extremely close to their host star may experience atmospheric escape due to the large amounts of high-energy radiation they receive. Understanding the conditions under which this occurs is critical, as atmospheric escape is believed to be a driving factor in sculpting planetary populations. In recent years, the near-infrared 10833 Å helium feature has been found to be a promising spectral signature of atmospheric escape. We use transmission spectroscopy to search for excess helium absorption in the extended atmosphere of WASP-48b, a hot Jupiter orbiting a slightly evolved, rapidly rotating F star. The data were collected using the Habitable-zone Planet Finder spectrograph on the Hobby-Eberly Telescope. Observations were taken over the course of seven nights, from which we obtain three transits. No detectable helium absorption is seen, as absorption depth is measured to -0.0025 ± 0.0021, or 1.2σ from a null detection. This nondetection follows our current understanding of decreasing stellar activity (and thus high-energy radiation) with age. We use a 1D isothermal Parker wind model to compare with our observations and find that our nondetection can best be explained with a low planetary mass-loss rate and high thermosphere temperature. We explore our results within the context of the full sample of helium detections and nondetections to date. Surprisingly, comparing helium absorption with the stellar activity index $\mathrm{log}\ {R}_{\mathrm{HK}}^{{\prime} }$ reveals a large spread in the correlation between these two factors, suggesting that there are additional parameters influencing the helium absorption strength.