Regenerative transient spectral hole frequency references have provided relative optical stability, measured by the Allan deviation, on the 10−13 scale. These references are comparatively insensitive to vibration and, unlike traditional Fabry–Perot cavities, atomic references, or gated spectral holes, the reference shape and position can depend on the laser input as well as the material properties. Numerical modeling of a frequency stabilization system incorporating regenerative spectral holes has been carried out, and the importance of the specific spectral hole-burning material has been considered. It is shown that for intervals shorter than the spectral hole lifetime, the hole reference is similar to a Fabry–Perot cavity reference. For periods longer than the hole lifetime or inverse rate of spectral diffusion, the performance of the spectral hole reference can be affected by uncompensated offsets in the stabilization system caused by the environment. Quantifying each effect demonstrates which are important and determines the pathway to development of improved reference materials.