In the UCD, unless it is/was a "Special Pick", it takes about 4 weeks for a car to come back. At the moment, PD appears to be reshuffling that rotation.
In the LCD/Hagerty's, unless it it/was a "Special Pick", or one of the 3 cars needed for one of the trophies (Ferrari 330 P4, Ford Mark IV, and Jaguar XJ13), it takes close to 3 months for a car to return in the rotation. Each of the "trophy three" show up roughly once a month.