Is one who is delayed in returning to his family, due to the sponsor's procrastination in approving his leave, despite his many attempts to persuade him, sinful?

It is the wife's right that her husband not be absent from her for more than six months, except with her permission, based on what was narrated from Umar, may Allah be pleased with him. Imam Ahmad, may Allah have mercy on him, made an exception for travel for Hajj, or for military expeditions (Ghazw), or for earning a livelihood for the family, provided the wife is self-sufficient and has a mahram who can care for her.

Therefore, if your absence is to seek lawful provision that you cannot find in your country, there is no sin in exceeding this period, and it is recommended to inform your wife of this. However, if means of livelihood are readily available in your country, then it is not permissible to be absent for more than six months except with the wife's permission.

It is recommended not to be away from one's wife and children for long periods in these times.