Unfortunately, this is quite common and a combination of stress, hormonal changes and children leaving home can be a major part of the problem.
In cases such as this it is important for her to see the doctor, severe hormonal swings can cause depression and some kind of hormonal medication such as HRT may be needed (antidepressants rarely work in this case so your wife is right about not wanting them!).
If it is a hormonal problem it is unlikely to resolve itself quickly so why not try and get the help of a female friend or relative who can broach this with her gently and encourage her to see the doctor.
This is not normally a permanent state but could last several years without treatment. I do hope that things sort themselves out for you.