U.S. farms have faced worker shortages for years. Now compounding the problem: The children of farmworkers are leaving the fields, forcing farm owners to look to other countries for labor.

The number of H-2A visas for seasonal farmworkers issued each year has more than quadrupled over the past decade. The growth has alarmed labor advocates. Farmers don't love the program, either.

Farmers in Georgia have been impacted by a multitude of events in the last few years: hurricanes, stalled aid, trade policy and, on top of that, drought...