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 telescopes 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.
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