There are people with a genetic error of metabolism called pyroluria who lose zinc (along with B6) thru the urine.
This is due to a defect in the manufacture of heme in the liver. By products called pyrroles are made which in themselves are not a problem, but they complex out B6 and zinc from the blood and make them unavailable to the body.

Treatments include testing for zinc/copper ratio, and then treatment with zinc supplements. Pyroluria may be present in up to 10% of people, silently. It is thought to increase anxiety and craving for alcohol.

http://drkaslow.com/html/pyroluria.html

Zinc treatment should be tested/monitored with blood work. A simple urine screening done by special labs can ID the disorder. No RX is needed for this test. But treatment should be supervised by a doctor, if the screening shows high pyrroles in the urine. High zinc intake needs to be balanced with copper, because if the ratio changes, low copper can become serious.

Also some common drugs deplete zinc. ACE inhibitors (some here on PD use these) for blood pressure are one family that deplete zinc from the body. People using acid blocking drugs may also become low in zinc because acid is needed to absorb zinc properly. Hormones, diuretics, and steroids will also deplete zinc over time.