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How can memories be maintained from days to a lifetime, given turnover of proteins that underlie expression of long-term synaptic potentiation (LTP)? One likely solution relies on synaptic positive feedback loops, prominently including persistent activation of CaM kinase II (CaMKII) and self-activated synthesis of protein kinase M zeta (PKM). Recent studies also suggest positive feedback based on recurrent synaptic reactivation within neuron assemblies, or engrams, is necessary to maintain memories. The relative importance of these feedback mechanisms is controversial. To explore the likelihood that each mechanism is necessary or sufficient, we simulated LTP maintenance with a simplified model incorporating persistent kinase activation, synaptic tagging, and preferential reactivation of strong synapses, and analyzed implications of recent data. We simulated three model variants, each maintaining LTP with one feedback loop: self-activated PKM synthesis (variant I); self-activated CamKII (variant II); and recurrent reactivation of strengthened synapses (variant III). Variant I requires and predicts that PKM must contribute to synaptic tagging. Variant II maintains LTP and suggests persistent CaMKII activation could maintain PKM activity, a feedforward interaction not previously considered. However we note data challenging this feedback loop. In variant III synaptic reactivation drives, and thus predicts, recurrent or persistent activity elevations of CamKII and other necessary kinases, plausibly contributing to empirically persistent elevation of PKM levels. Reactivation is thus predicted to sustain recurrent rounds of synaptic tagging and incorporation of plasticity-related proteins. We also suggest (model variant IV) that synaptic reactivation and autonomous kinase activation could synergistically maintain LTP. We propose experiments that could discriminate these maintenance mechanisms.