I've talked to her repeatedly and nothing
Well talking to her repeatedly will get you nothing if you do not go find some quests to do, or finish some you already have. You have to change something if the Jarl's steward is not offering you something to buy. The quest you might not have done could have nothing to do with Falkreath, it could just be a fetch quest or go kill this quest that you got else where. If not ask around Falkreath and see if there is something you can do that you missed.
If you still get nothing for your trouble, if you have not done the civil war questline you could do it as a Stormcloak and be made Thane under a different Jarl.