Should a pastor resign if his grown child backslides?

If anyone is above reproach, the husband of one wife, and his children are believers and not open to the charge of debauchery or insubordination (Tit 1:6).

Some Christians think this means that if a pastor's adult son or daughter strays from the faith, he should resign the pastorate. Several problems with that inference.

i) It gives the text a more specific meaning than the text states. The text doesn't specify that this includes both underage children and grown children. Although the wording of the text doesn't rule that out, it doesn't spell that out, either. 

ii) Most commands and prohibitions have an implied context. We need to ask what kind of situation they envision. Commands and prohibitions typically deal with common situations rather than exceptional situations. 

iii) Apropos (ii), the passage doesn't imply that an elder must have children. For instance, what if his children died? Child mortality was high back then. Disease. A fatal accident. Snakebite. Famine. 

Rather, it means that if he has children, then they should be believers (or faithful). It's dealing with a typical situation rather than every conceivable situation.

Likewise, Paul presumably doesn't mean to exclude a widower or celibate man from eldership. The statement is not intended to cover every possible case, but normal situations. By the same token, there's no reason to assume it's talking about "children" in general. 

iv) Fathers have no direct or ultimate control over whether or not their children will be believers. That's in God's hands.

By contrast, fathers, especially in the ancient world, where paternal authority was strong, had considerable control over the behavior of minors living under their roof. 

v) To make eldership contingent on the spiritual condition of adult children would subvert paternal authority. Instead of making children subject to the father, it makes the father subject to children. It makes the father's ministry dependent on the attitude of his grown children. But does Paul really intend to undermine paternal (and pastoral) authority in that way?

vi) Likewise, there's the well-worn distinction between apostates and backsliders. Should an elder resign the moment a grown child strays from the faith, even if that turns out to be temporary?  

vii) Christians who draw that inference seem to have this situation in mind: two Christians marry and raise their kids in a Christian home. Indoctrinate their kids in the faith. Take them to church from birth. But when they are grown, one or more of them stray from the faith.

Problem that scenario is that it's anachronistic in the context of mid-1C churches. It's not like these had been around for decades. Many of them were planted just a few years earlier by an apostle or missionary. They hadn't been attended for two or three generations. 

In addition, many or most of the Christians were fairly recent converts to Christianity. Former pagans. And in many cases, their grown children were raised in paganism. 

At best you have a father and/or mother who converts to Christianity, then begins to raise the younger kids in the new-found faith. But it may well be too late for the adult kids. The parents can witness to them, but they can't start from scratch. 

I'd add that that situation can easily be duplicated in many parts of the world today, including unchurched Americans.

viii) Finally, modern-day fathers in the West don't have the same authority their ancient counterparts did. So it's harder for them to keep their kids in check. Our culture undermines parental authority at every turn.