The long-time correlations of fluctuations of lattice displacements in the quantum paraelectrics and are studied within the framework of the mode-coupling theory of the dynamic transition from an ergodic to a non-ergodic state caused by defects. It is shown that the very hard local non-symmetry-breaking defects formed by the oxygen vacancies can induce the dynamic transition at . The low-temperature non-ergodic state is characterized by long-time correlations of local fluctuations of the polar displacements, which continuously arise for . Simultaneously, the local non-symmetry-breaking defects lead to the appearance of long-time correlations of long-wavelength fluctuations of acoustic displacements via the local random piezoelectric coupling for . The random local piezoelectric coupling is caused by the electrostrictive interaction, which is modified by the random electric fields of the frozen symmetry-breaking defects. The conditions that must be met for the dynamic transition to be induced by the oxygen vacancies are analysed. It is also shown that the unavoidable oxygen vacancies in the nominally pure and are quite sufficient in number to cause the non-ergodic state. The role of the dynamic transition in the formation of the glass state for lightly doped and is discussed.