Can gravity ever "run out"? Like for instance if you make gravitational slingshot maneuvers around a planet with rockets built somewhere else or even asteroids, over and over again, each slingshot accelerates the object, doesn't that mean its "taking" energy from the planet?

When an object "makes use of" gravitational potential energy, that means the force of gravity is doing work on that object if it moves in a favorable direction relative to the gravitational pull, right? That energy it gains has to come from somewhere, no?