If an opponent plays a card such as Local Unrest and targets my last ground force on the planet, that planet is turned neutral. When that happens, do I lose any PDS's and Space Docks on that planet, or do they remain? If my forces remain there, do I regain control when I land ground forces there again?
The Space Docks and PDS units are destroyed.
From page 3 of the official FAQ version 2.3
And for good measure, on page 12 of the rulebook: