Forgery

Can a wife sign her husband's name on a request for medical information without his permission? Can a wife be legally responsible if her husband later says he didn't consent? What if the wife states that she has signed husband's name many times before with permission.

Many hospitals may simply let a spouse have access to medical records even absent a living will. What the husband should do is sign a living will (statement of medical wishes) and health care proxy (authorization of an agent to take health care actions) and name the people he does trust. Since his spouse will be presumed to have authority by many, he should expressly state that she should not have authority if he doesn't want it. Husband should consult with an estate planning specialist in his state to address this (be careful of the cheap pre-printed forms, they are unlikely to address the somewhat unique facts you raise).

If the wife has signed many times before and the husband knows and did nothing he may be prevented from taking action against her since he did not object in the past.

As with so many legal questions, this could result in a different answer depending on state law. But the husband should take affirmative actions to assure that his wishes are carried out. If the marriage is faltering (which is what the question seems to imply) the husband should check with a family lawyer --- if they separate or he files for divorce any state laws that grant the wife authority (if they in fact do) may be negated by the filing for divorce, or legal separation. A family lawyer in your state would have to address this issue.