A positive test charge only has potential energy if there's a negative charge out there somewhere, attracting it.
As long as the positive charge is not right up close to the beckoning negative charge, it'll spring in that direction if you let it.
So the positive test charge doesn't run out of potential energy until it reaches the place of its heart's desire ... as far from other positive charges as it can get, AND up against or on top of the nearest negative charge.
