Gene Witmer is a philosopher at the University of Florida who has recently written a paper critiquing presuppositionalism. It appears that the paper is not a formal paper intended for publication in its current form, but rather is a preprint prepared for a "talk" to the Atheist, Agnostic and Freethinking Student Association at the University of Florida.
I have always had mixed feelings about taking presuppositionalism seriously. On the one hand, it appears that presuppositionalism is not taken seriously by the majority of Christian philosophers, as evidenced by the conspicuous absence of any articles defending the transcendental argument for God's existence in respected journals like Faith and Philosophy. On the other hand, there are many Christian apologists who use a presuppositionalist approach in debates with atheists, so a hard-hitting critique of presuppositionalism is a useful resource for atheist debaters.
While I think the overall quality of the essay is good, I did notice at least two problems.
1) Witmer quotes Paul Copan on the relationship between atheism and morality, in a way that implies that Copan is a presuppositionalist. I'm 95% confident that Copan is not a presuppositionalist, so in that sense the article is a bit misleading. On the other hand, it would not be too difficult to find similar quotations from bona fide presuppositionalists, so Witmer's general points still stand.
2) Witmer lambasts Barker's debate performance against Manata as "terrible," but he never really gave specific reasons to justify that rating of Barker's performance. In fact, he didn't discuss Barker's arguments at all! I haven't seen or heard that debate, so it is possible that Barker's performance was "terrible." Since Witmer doesn't give details, however, it is impossible assess Witmer's reasons for that assessment.