Is it permissible for a wife to seek divorce from her husband due to his failure to provide for her, except when he is present with her?

A husband must financially support his wife, and he is not permitted to refrain from doing so unless there is a legitimate شرعي reason, such as insubordination (nushooz). If he refrains from providing support during his absence, the wife has the right to seek divorce. However, it is advisable to discuss the matter with him first, as the issue might be resolved, and seeking divorce may not always be in her best interest.