While fully participating in Apostolic succession, the bishops of the very early church were in a position that was poorly defined with roles that often conflicted with those of deacons. In addition they were often elected by the people rather than appointed by the Pope. Some at the time thought this would help to ensure that good men were chosen.
Besides the short life expectancy of the time, bishops also encountered death due to persecution and assassinations.
While I can’t yet find an example, I believe there were bishops who resigned during the heresies that afflicted the Church in the first few centuries. We have to remember that the Church at this time was working to define itself and its core beliefs. This struggle meant considering not only the beliefs that we hold today, but also many heretical alternatives. (Jesus is God AND man, Jesus is God NOT man, Jesus is man, not God) Many of the bishops were right in the middle of this struggle.
Some bishops were unwilling to change their heretical beliefs and were excommunicated. Some split from the church in a schism over a belief and de facto resigned or became excommunicated. There were times when some bishops were excommunicated, then reunited, and then excommunicated!
This era was difficult, but indispensable to the Church since it gave the Church the opportunity to develop its theology embodied in the Creed.