Since their conception half a century ago, Hebbian cell assemblies have become a basic term in the neurosciences, and the idea that learning takes place through synaptic modifications has been accepted as a fundamental paradigm. As synapses undergo continuous metabolic turnover, adopting the stance that memories are engraved in the synaptic matrix raises a fundamental problem: How can memories be maintained for very long time periods? We present a novel solution to this long-standing question, based on biological evidence of neuronal regulation mechanisms that act to maintain neuronal activity. Our mechanism is developed within the framework of a neural model of associative memory. It is operative in conjunction with random activation of the memory system and is able to counterbalance degradation of synaptic weights and normalize the basins of attraction of all memories. Over long time periods, when the variance of the degradation process becomes important, the memory system stabilizes if its synapses are appropriately bounded. Thus, the remnant memory system is obtained by a dynamic process of synaptic selection and growth driven by neuronal regulatory mechanisms. Our model is a specific realization of dynamic stabilization of neural circuitry, which is often assumed to take place during sleep.