Sounds are represented in the mouse auditory cortex in the form of a representational map, in which the similarity of global activity patterns elicited by a pair of sounds encodes their perceptual relationship. Interestingly, sensory processing in cortex is generally robust despite loss of neurons during aging, and even the accelerated loss during prodromal phases of neurodegeneration. Here, we probed the robustness of the representational map against the permanent removal of specific neurons and tested in how far its structure is stabilized by homeostatic network mechanisms. We combined longitudinal two-photon calcium imaging of population responses evoked by a diverse set of sound stimuli with a targeted microablation of functionally characterized individual neurons. Unilateral microablation of 30 - 40 selected highly sound-responsive neurons in layer 2/3 induced a temporary disturbance of the representational map that, however, recovered in the course of 3-5 days. At the level of individual neurons, we observed that the recovery was predominantly driven by neurons, which were unresponsive to the sounds before microablation but gained responsiveness afterward, through strengthening the correlation structure of the local network. On the other hand, selective microablation of inhibitory neurons triggered a prolonged disturbance of the representational map that was primarily characterized by a reduction of the trial-to-trial reliability of sound responses. Collectively, our findings provide a link between the plasticity of individual neurons and the structure of a representational map at the population level revealing homeostatic network mechanisms safeguarding sensory processing in neocortical circuits.