I'll write more on this subject when I feel like it down the road at some point. I wanted to quickly jot down one reason why these examples don't really affect those of us who are indeterminists about free choices and our adherence to the Principle of Alternate Possibilities (PAP). Frankfurt counterexamples require that some controlling agent have access to the the mind of a creature where they are able to see prior states that would give some "tell" about what the chooser will in fact choose. Since they can see this, they would be able to flip a switch or something to cause the person to choose differently if the person isn't going to choose to their liking. If the controller doesn't have to flip the switch (because the chooser is going to choose according to the liking of the controller) then the person is still responsible for the choice, since no coercion was applied.
Here's one reason why this fails. Indeterminists claim that there can be no prior states that give the "tell" that the Frankfurt examples use. As William Vallicella points out, "Suppose Black has all the powers of a Laplacean demon: in a deterministic universe he can predict any state from any temporally prior state. These powers won't help him, however, in an indeterministic universe. Before Jones chooses, Black cannot predict what he will choose" (found here). In other words, we must assume that compatibilism is possible in order to grant that these Frankfurt counterexamples even have a chance at disrupting our confidence in the PAP. But in an indeterminisic universe, the controller has no way of definitively knowing what the chooser will choose. He has to wait for the choice to be made. In that case, libertarian free will (LFW) exists, there is simply a coercive agent who will make the chooser do what he didn't choose if he uses his LFW in a way that is displeasing to the controller.