Synaptic plasticity is widely believed to constitute a key mechanism for modifying functional properties of neuronal networks. This belief implicitly implies, however, that synapses, when not driven to change their characteristics by physiologically relevant stimuli, will maintain these characteristics over time. How tenacious are synapses over behaviorally relevant time scales? To begin to address this question, we developed a system for continuously imaging the structural dynamics of individual synapses over many days, while recording network activity in the same preparations. We found that in spontaneously active networks, distributions of synaptic sizes were generally stable over days. Following individual synapses revealed, however, that the apparently static distributions were actually steady states of synapses exhibiting continual and extensive remodeling. In active networks, large synapses tended to grow smaller, whereas small synapses tended to grow larger, mainly during periods of particularly synchronous activity. Suppression of network activity only mildly affected the magnitude of synaptic remodeling, but dependence on synaptic size was lost, leading to the broadening of synaptic size distributions and increases in mean synaptic size. From the perspective of individual neurons, activity drove changes in the relative sizes of their excitatory inputs, but such changes continued, albeit at lower rates, even when network activity was blocked. Our findings show that activity strongly drives synaptic remodeling, but they also show that significant remodeling occurs spontaneously. Whereas such spontaneous remodeling provides an explanation for "synaptic homeostasis" like processes, it also raises significant questions concerning the reliability of individual synapses as sites for persistently modifying network function. Author Summary Top Neurons communicate via synapses, and it is believed that activity-dependent modifications to synaptic connections—synaptic plasticity—is a fundamental mechanism for stably altering the function of neuronal networks. This belief implies that synapses, when not driven to change their properties by physiologically relevant stimuli, should preserve their individual properties over time. Otherwise, physiologically relevant modifications to network function would be gradually lost or become inseparable from stochastically occurring changes in the network. So do synapses actually preserve their properties over behaviorally relevant time scales? To begin to address this question, we examined the structural dynamics of individual postsynaptic densities for several days, while recording and manipulating network activity levels in the same networks. We found that as expected in highly active networks, individual synapses undergo continual and extensive remodeling over time scales of many hours to days. However, we also observed, that synaptic remodeling continues at very significant rates even when network activity is completely blocked. Our findings thus indicate that the capacity of synapses to preserve their specific properties might be more limited than previously thought, raising intriguing questions about the long-term reliability of individual synapses.