The RAPid Telescopes for Optical Response (RAPTOR) observatory network consists of several astronomical telescopes designed to search for astrophysical transients called gamma-ray bursts (GRBs). Although intrinsically bright, GRBs are difficult to detect due to their short durations, and as such, the RAPTOR telescopes must operate autonomously, at high duty-cycles and in peak operating condition. To facilitate more efficient planning of maintenance schedules, a recent research effort at Los Alamos National Laboratory (LANL) has focused on developing a structural health monitoring (SHM) system for these telescopes. This paper summarizes the results from this effort. The damage scenario of concern, namely damage to the telescope drive mechanism, is first presented. Next, a damage detection algorithm is developed with LANL's new publically available software package, SHMTools and the results of this process are discussed in detail. The paper then concludes with a summary of future planned refinements of the RAPTOR SHM system.