GitHub's failover problems have never been load-related. GitHub has pairs of fileservers where one is the master and the other's sole job is to follow along with the master and take over if it thinks the master is down, so when they do failover, it is to a node with just as much capacity as the previous master.

All the failover problems I can think of since they moved to this architecture 4 years ago have been coordination problems where something undesired happened when transitioning from one member of a pair to another. In this case, network problems lead them to a state where both members of a pair thought they were the master.