Memories are known to reactivate during sleep. A recent modelling study (Fauth & van Rossum, eLife, 2019) could reproduce this based on self-reactivations of heavily interconnected cell assemblies and showcased its beneficial consequences for memories. However, to be maintained, the memories needed frequent reactivations such that the weights within the assemblies remain at a high level. In this work, we extend the model such that memories are maintained independently of reactivations. We suggest that long-term memories are mainly represented by the number of connections between assembly neurons, and less dependent on the actual weight of these connections. We test this with simulations and (mean-field) analyses in recurrent networks, in which connections are subject to (1) structural plasticity, which creates and removes connections via stochastic processes, (2) synaptic plasticity adapting the synaptic weights according to neural activity and (3) a biologically inspired spontaneous dynamics of the synaptic weight. We show that, after extended periods without reactivations, memories can have three different states depending on their connectivity: At relatively high degrees of connectivity, memories can reactivate themselves. At slightly lower degrees of connectivity, memories can only be reactivated by external stimuli but may self-reactivate in a short time span afterwards. At even lower degrees of connectivity, memories cannot be reactivated by external stimuli at all. In this case, the structural connections of the memory still exist for extended periods and can be used to relearn the pre-existing memory very fast. This provides a possible explanation for Ebbinghaus’ savings effect. Hereby the connectivity of newly learned assemblies relies mainly on strong synaptic weights, whereas older assemblies rely on a large number of synapses. Thus, interference with the reactivations (i.e. sleep deprivation), existing synapses, or synaptogenesis will impact new memories more severely than older ones, which may explain the gradedness of retrograde amnesia.