  We search for microvariability in a sample of 485 Mira variables with high
quality I-band light curves from the second generation Optical Gravitational
Lensing Experiment (OGLE-II). Rapid variations with amplitudes in the ~0.2-1.1
mag range lasting hours to days were discovered in Hipparcos data by de Laverny
et al. (1998). Our search is primarily sensitive to events with time-scales of
about 1 day, but retains a few percent efficiency (per object) for detecting
unresolved microvariability events as short as 2 hours. We do not detect any
candidate events. Assuming that the distribution of the event time profiles is
identical to that from the Hipparcos light curves we derive the 95% confidence
level upper limit of 0.038 per year per star for the rate of such events (1 per
26 years per average object of the ensemble). The high event rates of the order
of 1 per year per star implied by the Hipparcos study in the H_P band are
excluded with high confidence by the OGLE-II data in the I band. Our
non-detection could still be explained by much redder spectral response of the
I filter compared to the H_P band or by population differences between the
bulge and the solar neighborhood. In any case, the OGLE-II I-band data provide
the first limit on the rate of the postulated microvariability events in Mira
stars and offer new quantitative constraints on their properties. Similar
limits are obtained for other pulse shapes and a range of the assumed
time-scales and size-frequency distributions.
