Abstract: EicC is a highly polarized electron-ion collider proposed by the Institute of Modern Physics, Chinese Academy of Sciences. The center of mass collision energy is between 15-20 GeV. EicC aims at a peak luminosity of 2×10³³ cm^-2·s^-1 for electron-proton collision. In the electron-proton collision mode, the electron ring (eRing) and proton ring (pRing) of EicC have 256 and 448 bunches, respectively. Since the number of bunches in the two rings is different, when some bunches in one beam are missing, the effect of the missing bunches will be transmitted to multiple electron and proton bunches through beam-beam interactions, which may cause instability. In order to investigate the effect of missing bunches on the beam stability, self-consistent beam-beam effect simulations were performed using the AthenaGPU program, and the dipole instability was analyzed under linear approximation using the AthenaMatrix program. In the case of missing electron bunches, the simulation results show that missing any number of bunches does not cause beam instability but only affects the luminosity at equilibrium and the luminosity degradation rate. After scanning the electron beam-beam parameter using the matrix method, the results show that the instability growth rate in the horizontal direction is the same as that without missing electron bunches, regardless of the number of missing bunches. The vertical instability growth rate decreases as the number of missing bunches increases. Under the current beam parameters and only considering the effect of missing bunches on beam instability, EicC allows any number of electron bunches to be missing. The dipole instability occurs in the vertical direction when one proton bunch is missing. When two proton bunches are missing, quadrupole instability occurs in the horizontal direction, and after the amplitude of the quadrupole oscillation increases to a large value, the bunch centroid also starts to oscillate. When three proton bunches are missing, the beams show dipole instability in the vertical direction, similar to the case in which one proton bunch is missing, and quadrupole instability in the horizontal direction, similar to the case in which two proton bunches are missing. When more proton bunches are missing, no instability is observed in the simulation, but the luminosity is lower than expected. The above instabilities that appear in the horizontal and vertical directions can be avoided by adjusting the electron beam’s horizontal and vertical nominal tunes to 0.60 and 0.58, respectively. Although the dipole or quadrupole instability can be avoided by adjusting the nominal tunes to move the beams out of the instability region, it does not necessarily suppress the negative effect of missing bunches on bunch size.