It is now known that astrocytes modulate the activity at the tripartite synapses where indirect signaling via the retrograde messengers, endocannabinoids, leads to a localized self-repairing capability. In this paper, a self-repairing spiking astrocyte neural network (SANN) is proposed to demonstrate a distributed self-repairing capability at the network level. The SANN uses a novel learning rule that combines the spike-timing-dependent plasticity (STDP) and Bienenstock, Cooper, and Munro (BCM) learning rules (hereafter referred to as the BSTDP rule). In this learning rule, the synaptic weight potentiation is not only driven by the temporal difference between the presynaptic and postsynaptic neuron firing times but also by the postsynaptic neuron activity. We will show in this paper that the BSTDP modulates the height of the plasticity window to establish an input-output mapping (in the learning phase) and also maintains this mapping (via self-repair) if synaptic pathways become dysfunctional. It is the functional dependence of postsynaptic neuron firing activity on the height of the plasticity window that underpins how the proposed SANN self-repairs on the fly. The SANN also uses the coupling between the tripartite synapses and γ -GABAergic interneurons. This interaction gives rise to a presynaptic neuron frequency filtering capability that serves to route information, represented as spike trains, to different neurons in the subsequent layers of the SANN. The proposed SANN follows a feedforward architecture with multiple interneuron pathways and astrocytes modulate synaptic activity at the hidden and output neuronal layers. The self-repairing capability will be demonstrated in a robotic obstacle avoidance application, and the simulation results will show that the SANN can maintain learned maneuvers at synaptic fault densities of up to 80% regardless of the fault locations.