The sense that irony doesn't work is unfortunately an ideological trick. The really point is that it cannot work. Zizek was quickly on to the problem of Irony in his The Sublime Object of Ideology; "in contemporary societies, democratic or totalitarian, that cynical distance, laughter, irony, are, so to speak, part of the game. The ruling ideology is not meant to be taken seriously or literally." (p24)
Which is to say that "the ruling culture" deals with irony through recognition "it takes into account" through cynicism (p26).
This cynicism is a means of ensuring that the ideological systems of the ruling culture continue to function in the face of criticism. Zizek again: "It is clear, therefore, that confronted with such cynical reason, the traditional critique of ideology no longer works. We can no longer subject the ideological text to 'symptomatic reading', confronting it with its blank spots, with what it must repress to organize itself, to preserve its consistency - cynical reason takes this distance into account in advance." (p26-7).
We cannot turn irony on the 'ruling culture' because it has been incorporated into that ruling culture. Ideology is "no longer meant, even by its authors, to be taken seriously - its status is just that of a means of manipulation, purely external and instrumental; its rule is secured not by its truth-value but by simple extra-ideological violence and promise of gain"(p27). Irony is thus a direct support to the repressive state apparatus because it warns of its impending use.