Vehicle-to-grid increases the low utilization rate of privately owned electric vehicles by making their batteries available to the electricity grid. We formulate a robust optimization problem in continuous time that maximizes the expected profit from selling primary frequency regulation to the grid and guarantees that vehicle owners can meet their market commitments for all frequency deviation trajectories in an uncertainty set that encodes applicable EU legislation. Faithfully modeling the energy conversion losses during battery charging and discharging renders this optimization problem non-convex. By exploiting a total unimodularity property of the proposed uncertainty sets and an exact linear decision rule reformulation, we prove that this non-convex robust optimization problem in continuous time is equivalent to a tractable linear program. Through extensive numerical experiments based on real-world data we investigate how the value of vehicle-to-grid depends on the penalties for non-delivery of promised regulation power, the delivery guarantees, and the vehicle's battery, charger, and yearly mileage.