Is it permissible for me to shun my brother after confronting him three times, if I only see him once a week, or must I adhere to the three-day limit only?

The basic rule regarding a Muslim forsaking his brother is that it is not permissible for more than three nights, unless it is on account of a sin, and there is a hoped-for benefit from the forsaking, such that the wrongdoer abandons it. In this case, forsaking becomes permissible. However, if it is merely a difference in viewpoints, then forsaking is not allowed. What is obligatory is to advise the one who differs, to be patient with him, and to overlook his slips.