The mechanisms of long-term synaptic maintenance are a key component to understanding the mechanism of long-term memory. From biological experiments, a hypothesis arose that repetitive stimuli with appropriate intervals are essential to maintain new synapses for periods of longer than a few days. We successfully reproduce the time-course of relative numbers of synapses with our mathematical model in the same conditions as biological experiments, which used Adenosine-3', 5'-cyclic monophosphorothioate, Sp-isomer (Sp-cAMPS) as external stimuli. We also reproduce synaptic maintenance responsiveness to intervals of Sp-cAMPS treatment accompanied by PKA activation. The model suggests a possible mechanism of sustainable synaptogenesis which consists of two steps. First, the signal transduction from an external stimulus triggers the synthesis of a new signaling protein. Second, the new signaling protein is required for the next signal transduction with the same stimuli. As a result, the network component is modified from the first network, and a different signal is transferred which triggers the synthesis of another new signaling molecule. We refer to this hypothetical mechanism as network succession. We build our model on the basis of two hypotheses: (1) a multi-step network succession induces downregulation of SSH and COFILIN gene expression, which triggers the production of stable F-actin; (2) the formation of a complex of stable F-actin with Drebrin at PSD is the critical mechanism to achieve long-term synaptic maintenance. Our simulation shows that a three-step network succession is sufficient to reproduce sustainable synapses for a period longer than 14 days. When we change the network structure to a single step network, the model fails to follow the exact condition of repetitive signals to reproduce a sufficient number of synapses. Another advantage of the three-step network succession is that this system indicates a greater tolerance of parameter changes than the single step network.