We propose a design methodology to facilitate fault tolerance of deep learning models. First, we implement a many-core fault-tolerant neuromorphic hardware design, where neuron and synapse circuitries in each neuromorphic core are enclosed with astrocyte circuitries, the star-shaped glial cells of the brain that facilitate self-repair by restoring the spike firing frequency of a failed neuron using a closed-loop retrograde feedback signal. Next, we introduce astrocytes in a deep learning model to achieve the required degree of tolerance to hardware faults. Finally, we use a system software to partition the astrocyte-enabled model into clusters and implement them on the proposed fault-tolerant neuromorphic design. We evaluate this design methodology using seven deep learning inference models and show that it is both area- and power-efficient.