If a husband and wife are having marital issues which leads the wife into depression is she still obliged to fulfill the husbands right to intimacy?
The wife has been denied her emotional and mental rights from the husband which has lead her to a weak mental state

By default she must make herself available for intimacy, but if he is causing her psychological and mental harm, and the way for her to protect herself from this harm is to deny him intimacy, then yes in this case she can.