  We present the results of a systematic search for outbursts in the narrow
positron annihilation line on various time scales (5x10^4 - 10^6 s) based on
the SPI/INTEGRAL data obtained from 2003 to 2008. We show that no outbursts
were detected with a statistical significance higher than ~6 sigma for any of
the time scales considered over the entire period of observations. We also show
that, given the large number of independent trials, all of the observed spikes
could be associated with purely statistical flux fluctuations and, in part,
with a small systematic prediction error of the telescope's instrumental
background. Based on the exposure achieved in ~6 yr of INTEGRAL operation, we
provide conservative upper limits on the rate of outbursts with a given
duration and flux in different parts of the sky.
