We investigate the stability of MnPb2Bi2Te6 (MPBT), which is predicted to be a magnetic topological insulator (TI), using density functional theory calculations. Our analysis includes various measures such as enthalpies of formation, Helmholtz free energies, defect formation energies, and dynamical stability. Our thermodynamic analysis shows that the phonon contribution to the energy gain from finite temperature is estimated to be less than 10 meV/atom, which may not be sufficient to stabilize MPBT at high temperatures, even with the most favorable reactions starting from binaries. While MPBT is generally robust against the formation of various defects, we find that the anti-site defect formation of MnPb is the most likely to occur, with a corresponding energy less than 60 meV. This can be attributed to the significant energy cost from compressive strain at the PbTe layer. Our findings suggest that MPBT is on the brink of stability in terms of thermodynamics and defect formation, underscoring the importance of conducting systematic analyses of the stability of proposed TIs, including MPBT, for their practical utilization. This study offers valuable insights into the design and synthesis of desirable magnetic TI materials with robust stabilities.