A statistical approach is presented to estimate the stability of magnetic states of nano- and microstructures to thermal fluctuations and random external actions. It implies the construction of the multidimensional energy surface of a system, search for the minimum energy paths between locally stable states on this surface, and calculation of rates of magnetic transitions between corresponding magnetic configurations at arbitrary temperatures in the harmonic approximation of the transition state theory. Lifetimes of quasi-two-dimensional topologically protected magnetic structures have been studied. The effect of magnetic characteristics of a medium limited by the geometry of a sample, nonmagnetic defects, and external magnetic field on the lifetimes of topological magnetic states has been shown.