IEEE Nature-inspired neuromorphic architectures are being explored as an alternative to imminent limitations of conventional complementary metal-oxide semiconductor architectures. Utilization of such architectures for practical applications like advanced pattern recognition tasks will require synaptic connections that are both reconfigurable and stable. Here, we report realization of stable atomic-switch networks (ASNs), with inherent complex connectivity, self-assembled from percolating metal nanoparticles (NPs). The device conductance reflects the configuration of synapses, which can be modulated via voltage stimulus. By controlling Relative Humidity and oxygen partial-pressure during NP deposition, we obtain stochastic conductance switching that is stable over several months. Detailed characterization reveals signatures of electric-field-induced atomic-wire formation within the tunnel-gaps of the oxidized percolating network. Finally, we show that the synaptic structure can be reconfigured by stimulating at different repetition rates, which can be utilized as short-term to long-term memory conversion. This demonstration of stable stochastic switching in ASNs provides a promising route to hardware implementation of biological neuronal models and, as an example, we highlight possible applications in reservoir computing.