My wife has had a headache for a month now. What can it be?

See a neurologist. Hard to say without a complete evaluation. Probably best done by a headache specialist or neurologist.
Magnesium. If she's seen a neurologist and has not found relief, she should consider a program of aerobic exercise, biofeedback (or relaxation training), taking magnesium oxide 400 mg daily, coq10, 300 mg. Half of headache sufferers are deficient in magnesium. Here is an article on magnesium and headaches: http://www.Nyheadache.Com/index.Php?Option=com_content&view=article&id=39&itemid=76.
Hadache. Your headaches could be coming from tension, eye strain, tooth grinding, dehydration, lack of sleep/poor sleep, skipping meals, stress, sleep apnea/snoring, or chronic sinus problems.