Car dealerships are facing a roadblock: convincing workers in their 20s and 30s to work and stay in an auto retail business defined by long shifts, weekends on the selling floor, haggling and commission-based pay.

Nearly 60% of dealership hires are millennial workers, and more than half of those new hires turn over annually, according to a study by Hireology, a talent and management firm.

Millennials...