Of course, you can leave your hitch rack on your car all the time but it depends where you live and how much you use it. Some of us leave our racks on the car year-round without issue. These racks see a lot of rain, cross-country road trips, and bake in the sun, and they’re fine. That said, if you live somewhere it snows a lot in the winter or you’re not using it for months at a time, it’s probably better to take it off and keep it clean and dry rather than subject it to unnecessary abuse.
Most of these racks use an aluminum frame, but the hardware and hitch beam are usually steel. So, use your judgment. If everything else metal is rusting around you from salt air or road spray, you should probably hose it off and store it somewhere dry when not in use.