What is the ruling of Islamic law regarding a husband separating from his wife—without divorce—while continuing to bear his responsibilities towards her and their children, due to the wife's continuous complaints and deteriorating psychological state, along with the husband's repeated but unsuccessful attempts to improve the relationship?

It is advisable to turn to Allah in supplication, and to address the shortcomings they complain of by listening to their observations and trying to improve them. Separation is not a solution. The fundamental solution is to resort to a wise external party (a family counselor, or a sensible man) for advice and arbitration, and to seek psychological counseling if necessary. The noble Hadith (definition) states: "A believing man should not hate a believing woman; if he dislikes one of her characteristics, he will be pleased with another." Ibn Baz emphasizes that every human being has deficiencies, and he calls upon the wife to return and treat her husband kindly. The conclusion is to strive to make the marriage successful and save the children, and to manage defects and shortcomings. If that does not succeed, then the last resort is to release with kindness, but divorce should be a single pronouncement with the possibility of reconciliation during the 'iddah (definition) (waiting period).