What is the ruling on a wife abandoning her husband, refusing reconciliation, and refraining from speaking with him for a month?

Disagreements and estrangement occur between spouses, even between the Messenger of Allah (peace and blessings be upon him) and his wives. This is a natural and inevitable matter, but it must be addressed before it becomes difficult to resolve. The general principle is to prevent estrangement and to hold accountable the one who causes it. However, Islamic law permits a husband to shun his wife in bed or in speech if it is due to her disobedience (nushuz) and arrogance, and if admonition has been ineffective, so that she may be deterred.