My question pertains to elders and having believing children. If when they, believing children of an elder, leave home and happen to fall away from the church should the elder step down? Or does this fall under the example aspect and he should step down because of that?
Another question is what if he has two children and they both have left home, and one has fallen away from the church, should he step down?
In the qualifications for elders we read:
"One who rules his own house well, having his children in submission with all reverence (for if a man does not know how to rule his own house, how will he take care of the church of God?)" (I Timothy 3:4-5).
"having faithful children not accused of dissipation or insubordination" (Titus 1:6).
In both passages, the qualifications are presented as qualities that a man currently possesses. A man is not qualified if he once was "not soon angry" but at the moment has a terrible time with his temper.
A man’s children must be faithful, believers, or trustworthy. In the New Testament, the faithful are those who are Christians (Acts 10:45; 16:1; II Corinthians 6:15). The children are not just Christian in name, but they have shown themselves to be steadfast followers. By requiring the children to be faithful, the implication is that the elder has successfully raised children through all their stages of growth. Therefore, the elder has demonstrated consistency in overseeing his own household that has lasted for many years.
The children must not have charges against them of behaving like worldly people or unwilling to live by the laws of Christ. Such is expected of all Christians (I Peter 4:1-5; II Thessalonians 3:6) and an elder’s children must be able to show their ability to live the life of a Christian. The children should be obedient to their father as well as to Christ (Ephesians 6:1-3). They should demonstrate dignified respect for their father; a respect that is sincere and honest, and not one that is done simply for show.
It is upsetting to people that a man's qualifications for the eldership are based in part on the behavior of other people, but this is what God has laid out. There are qualifications for the elder's and deacon's wife in I Timothy 3:11. If an elder's wife became unfaithful, would we object and say she is her own person and the elder shouldn't be held accountable? It is possible that an elder's wife might leave him for another man, and that elder is completely innocent of the matter. Perhaps not often likely, but it is possible. Still, the man is no longer qualified to be an elder because he doesn't meet the qualifications given for the position.
Now consider this for a moment. If an elder is unable by his influence over his own children to keep them on the path of righteousness, would you want such a man in charge of the souls of others? "He who is faithful in what is least is faithful also in much; and he who is unjust in what is least is unjust also in much" (Luke 16:10).
If an elder's child leaves the church, that child is no longer faithful and can be accused of insubordination. That elder, responsible for the situation or not, is no longer qualified for the position of an elder. Hopefully, he will be able to work with his child and bring his child back to the Lord. If such is the case and he remains qualified in all other areas, then he can resume his duty as an elder for the Lord's people.