Synchrony in neuronal networks plays a crucial role in the functioning of the brain. Stability of synchrony is most desirable to prevent any emergent desynchrony due to natural events, internal or external disturbances. The brain might have its own mechanism to repair its desynchrony, otherwise, some external procedure might be necessary to restore synchrony. We propose here a mechanism to realize robust synchrony in neuronal networks against parameter drifting. A selective addition of cross-coupling links over and above the conventional diffusive coupling links is found [Saha et al. (2017)] recently that makes dramatic improvements in the stability of synchrony of dynamical networks and that saves synchrony against breakdown due to parameter drifting. We apply the concept to realize globally stable synchrony in neuronal networks and the desired effect of robust synchrony and, present our numerical studies with examples of network motifs and a larger network of neurons and using the Hindmarsh-Rose (HR) [Hindmarsh and Rose (1984)] slow-fast neuron model for each node of the networks.