Ethernet is a mature technology with millions of installations and years of proven reliable service. You are not very likely to have problems in the core networking technology if you follow basic wiring, network layout, and configuration principles. Nevertheless, the real-time audio application is a special case, and specific knowledge can help. We'll cover some general Ethernet and IP troubleshooting topics here, as well as those expressly oriented to AoIP and Livewire.
Before we get into troubleshooting, however, it should be noted that the best way to avoid downtime is to build the network well in the first place. Use high-grade cables, good-quality factory-made patch cords, etc. Be careful ...