Long-term synaptic plasticity exhibits distinct phases. The synaptic tagging hypothesis suggests an early phase in which synapses are prepared, or "tagged," for protein capture, and a late phase in which those proteins are integrated into the synapses to achieve memory consolidation. The synapse specificity of the tags is consistent with conventional neural network models of associative memory. Memory consolidation through protein synthesis, however, is neuron specific, and its functional role in those models has not been assessed. Here, using a theoretical network model, we test the tagging hypothesis on its potential to prolong memory lifetimes in an online-learning paradigm. We find that protein synthesis, though not synapse specific, prolongs memory lifetimes if it is used to evaluate memory items on a cellular level. In our model we assume that only "important" memory items evoke protein synthesis such that these become more stable than "unimportant" items, which do not evoke protein synthesis. The network model comprises an equilibrium distribution of synaptic states that is very susceptible to the storage of new items: Most synapses are in a state in which they are plastic and can be changed easily, whereas only those synapses that are essential for the retrieval of the important memory items are in the stable late phase. The model can solve the distal reward problem, where the initial exposure of a memory item and its evaluation are temporally separated. Synaptic tagging hence provides a viable mechanism to consolidate and evaluate memories on a synaptic basis.