The correct sentence that follows grammatical conventions is:
The radio station lost its license to broadcast in our town.
The other sentences incorrectly use "it's" (which is a contraction for "it is") instead of "its" (which denotes possession). Additionally, "Its difficult" should be "It's difficult" because it requires the contraction for "It is." The sentence "Soccer has lost it’s appeal for Jim because of his knee injury" also misuses "it’s."