Very Large Scale Integration (VLSI) based neuromorphic circuits also known as Silicon Neurons (SiNs) emulate the electrophysiological behavior of biological neurons. With the advancement in technology, neuromorphic systems also lead to various reliability issues and hence making their study important. Bias Temperature Instability (BTI) and Hot Carrier Injection (HCI) are the two major reliability issues present in VLSI circuits. In this work, we have investigated the combined effect of BTI and HCI on the two types of integrate-and-fire based SiNs namely (a) Axon-Hillock and (b) Simplified Leaky integrate-and-fire circuits using their key performance parameters. Novel reliability-aware AH and SLIF circuits are proposed to mitigate the reliability issues. Proposed reliability-aware designs show negligible deviation in performance parameters after aging. The time-zero process variability analysis is also carried out for proposed reliability-aware SiNs. The power consumption of existing and proposed reliability-aware neuron circuits is analyzed and compared.