Changes in the synaptic connection strengths between neurons are believed to play a role in memory formation. An important mechanism for changing synaptic strength is through movement of neurotransmitter receptors and regulatory proteins to and from the synapse. Several activity-triggered biochemical events control these movements. Here we use computer models to explore how these putative memory-related changes can be stabilised long after the initial trigger, and beyond the lifetime of synaptic molecules. We base our models on published biochemical data and experiments on the activity-dependent movement of a glutamate receptor, AMPAR, and a calcium-dependent kinase, CaMKII. We find that both of these molecules participate in distinct bistable switches. These simulated switches are effective for long periods despite molecular turnover and biochemical fluctuations arising from the small numbers of molecules in the synapse. The AMPAR switch arises from a novel self-recruitment process where the presence of sufficient receptors biases the receptor movement cycle to insert still more receptors into the synapse. The CaMKII switch arises from autophosphorylation of the kinase. The switches may function in a tightly coupled manner, or relatively independently. The latter case leads to multiple stable states of the synapse. We propose that similar self-recruitment cycles may be important for maintaining levels of many molecules that undergo regulated movement, and that these may lead to combinatorial possible stable states of systems like the synapse.