More than two-thirds of America's youth would fail to qualify for military service because of physical, behavioral or educational shortcomings, posing challenges to building the next generation of soldiers even as the U.S. draws down troops from conflict zones.

The military deems many youngsters ineligible due to obesity, lack of a high-school diploma, felony convictions and prescription-drug use for attention-deficit hyperactivity disorder. But others are now also running afoul of standards for appearance amid the growing...