Mass measurements from low-mass black hole X-ray binaries (LMXBs) and radio pulsars have been used to identify a gap between the most massive neutron stars (NSs) and the least massive black holes (BHs). BH mass measurements in LMXBs are typically only possible for transient systems: outburst periods enable detection via all-sky X-ray monitors, while quiescent periods enable radial velocity measurements of the low-mass donor. We quantitatively study selection biases due to the requirement of transient behavior for BH mass measurements. Using rapid population synthesis simulations ( COSMIC ), detailed binary stellar-evolution models ( MESA ), and the disk instability model of transient behavior, we demonstrate that transient LMXB selection effects introduce observational biases, and can suppress mass-gap BHs in the observed sample. However, we find a population of transient LMXBs with mass-gap BHs form through accretion-induced collapse of an NS during the LMXB phase, which is inconsistent with observations. These results are robust against variations of binary evolution prescriptions. The significance of this accretion-induced collapse population depends upon the maximum NS birth mass M NS , birth − max . To reflect the observed dearth of low-mass BHs, COSMIC and MESA models favor M NS , birth − max ≲ 2 M ⊙ . In the absence of further observational biases against LMXBs with mass-gap BHs, our results indicate the need for additional physics connected to the modeling of LMXB formation and evolution.