Studies were made into the arise and an evolution of the beam breakup (BBU) instability in a rectangular dielectric resonator under excitation by a sequence of relativistic electron bunches. The dielectric resonator is a section of a rectangular waveguide loaded by the two dielectric slabs (located along the wide side) and closed by the metal grids. A material of the slabs is teflon. A thickness of the slabs is 8.2 mm, a wide size and a length of the slabs are equal to the resonator wide size and length respectively. The metal grids are transparent for the charged particles and nontransparent for the excited electromagnetic fields. The wavelength of the LSM 2, 1, 12 (Longitudinal Section Magnetic) operating mode is 53.2 mm. The electron energy of bunches is 4.5 MeV, the charge of each bunch is 6.4 nC, the bunch repetition period is equal to twice the wavelength of the LSM 2, 1, 12 mode. By the use of numerical PIC simulations, the charge losses of electron bunches on the dielectric plates were investigated as the bunches were displaced relative to the cavity axis. It is found that the charge losses on the dielectric slabs due to the BBU instability do not exceed 5%. When the bunch repetition period is changed to a multiple of another eigenfrequency (eg, the LSM 1, 1, 12 mode), the charge losses of drive bunches do not change appreciably.