As much as I love Piper (quite a bit), and as big a difference as he has had in my life (probably as much or more than anyone), this is the biggest potential weakness I can see to the application of Christian Hedonism.
On the one hand Kant rejects the view that the test of a proposed maxim is whether obedience to it would in the end lead to the happiness of a rational being. Kant has no doubt that all men do indeed desire happiness; and he has no doubt that the highest good conceivable is that of the individual’s moral perfection crowned by the happiness which it merits. But he nonetheless believes that our conception of happiness is too vague and shifting to provide a moral guide.
After Virtue, Alasdair MacIntyre
It’s not a weakness that cannot be overcome; but it is vitally important to instruct people that happiness is not our moral guide, the revealed will of God is and we trust that will bring us happiness ultimately.
(As a postscript, it really is not a weakness in what Piper says, but in how he is interpreted.)