Primordial black holes (PBHs) are thought to have been formed as a result of density fluctuations in the very early Universe. It is suggested that PBHs of mass $\sim 5 \times 10^{14} \mathrm{\ g}$ or less have evaporated through the release of Hawking radiation by the present day. However, PBHs of initial mass $10^{15} \mathrm{\ g}$ should still be evaporating at the present epoch. Over the past few years, very high-energy (VHE; E $>$ 100 GeV) gamma-ray emission from PBHs in the form of a burst has been searched for using ground-based gamma-ray instruments. However, no observational evidence has been reported on the detection of VHE emission from PBHs yet. Previously, an upper limit on the rate density of PBHs was calculated using 750 hours of archival data taken between 2009 and 2012 by the VERITAS gamma-ray observatory. We will augment this study with additional data taken between 2012 and 2017. In addition to more data, the lower energy threshold on the newer data will help to produce an improved upper limit on the rate at which PBHs are evaporating in our local neighborhood. This work is still in progress, therefore we will only report an expected change to the upper limit on the rate density of PBH evaporation.