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Plasma discharge in the capillary is used to develop x-ray lasers, waveguides for high power laser pulses, and as active plasma lenses to focus high energy charged particle beams. Capillary discharges in the high repetition rate regime are of interest for applications that require large average values, such as luminosity and/or electric current of laser accelerated particles. In the present paper, we study the capillary discharge in the high repetition rate regime in connection with the ultrashort laser pulse guiding for laser electron acceleration. Using magnetohydrodynamic computer simulations and theoretical scaling, we investigate the filling of the capillary with the gas, the electric discharge development leading to outflow of the plasma from the capillary, and the recovery of gas distribution after the discharge end. In the next cycle, these processes are repeated. As a result, we found the characteristic cycle time, which determines the upper limit on the repetition rate allowed by the capillary parameters. In the case of the capillary discharges used for acceleration of sub-GeV electron beams, e.g., needed for compact free electron lasers, an upper limit on the repetition rate is approximately equal to 10 kHz.