A photometric monitoring campaign has been conducted in order to investigate the character and origin of flaring events occasionally seen in the long-term low-state light curve of the polar prototype AM Her. Four telescopes employed during 2004 May–July revealed that the events have typical duty cycles of 2%–35%, amplitudes of 0.2–0.6 mag, and typical durations of 15–90 minutes. A striking concentration of the 2004 events appears near inferior and superior conjunction of the secondary star. Interestingly, in the long-term RoboScope-monitored light curve (1990–2003), similar events are uniformly distributed in phase. AM Her's accretion geometry and the nature of its low states allow for two likely origins for the observed events, namely, residual accretion during low states and activity (flares) on the secondary star. Considering that AM Her is likely a one-pole accretor in the low states, the former requires irregular mass transfer from the secondary, resulting in random accretion bursts, with cyclotron beaming concentrating the flares into two phase intervals. On the other hand, considering the stability of the magnetic poles, this cannot address the random distribution of the events during the long-term light curve. Drifting active regions on the secondary star could explain the random distribution of the events; however, coincidence must be invoked to explain their occurrence at the observed phases of orbital conjunction. A combination of the two ideas is also discussed, in which stellar activity on the secondary star induces random accretion bursts, with cyclotron beaming then concentrating the flares into two phase intervals.