Most contemporary epistemologists aren't global skeptics, so most contemporary epistemologists are obliged to defend one of the above structural theories. Historically, a usual point of departure for such defenses has been a quick dismissal of infinitism by arguing that an infinite regress is somehow vicious. But in the past 15 years, infinitism has experienced increasing support in the philosophic community. Each philosopher has his own specific emphases and disagrees with others on certain points, but among others, Peter Klein, Scott Aikin, David Atkinson, Jeanne Peijnenburg, Jeremy Fantl, and John Turri have defended it.
As is often the case, however, the proponents of a theory are often the first to mention its weaknesses, even if unwittingly. For instance, in "Modest Infinitism" (link), Fantl writes:
It is true that infinitism (on my construal) will give no answer to the question of what degree of justification is required for knowledge. But infinitism is not the only epistemic theory with this difficulty. Any fallibilistic epistemic theory will have trouble specifying a non-arbitrary threshold for knowledge. Certainty is too high a threshold (because the theory is fallibilistic), and any degree of justification less than certainty seems arbitrary. To solve this problem we might want to say that the degree of justification required for knowledge varies according to non-epistemic features of your situation. The degree of justification required for knowledge would thus be determined by context (for example, your stake in the belief being true). Whether one is tempted by a view like this (and it is open to the infinitist to adopt it), the difficulty infinitism runs into in setting a threshold for knowledge is not unique to infinitism and therefore cannot be decisive against it. (pg. 559)
While I have seen Klein, Atkinson, and Peijnenburg make the same appeal to pragmatic contextualization to specify the degree threshold, I have yet to see anyone specify how to non-arbitrarily choose it. So Fantl's conclusion is ironic, given that Klein and others principally reject foundationalism for allegedly requiring that one arbitrarily choose what to hold as a basic belief. Even more ironic is the fact that earlier in his article, Fantl explains how a foundationalist can avoid arbitrarity, an explanation which is strikingly similar to what I have argued on this blog regarding necessary and sufficient conditions for knowledge:
We can ask why self-justifying reasons are self-justifying. If the traditional foundationalist has an answer, it seems like it must involve some metajustificatory feature. If the traditional foundationalist has no answer, it seems like the view has arbitrary foundations. (See BonJour, Structure, 30-3, for a similar argument.)
However, the traditional foundationalist can argue that completely self-justifying reasons are not self-justifying in virtue of some metajustificatory feature, nor are they arbitrary. It may be that certain reasons have to be assumed to be self-justifying if skepticism is to be avoided. This is a rather familiar form of rationalist argument for the existence of a priori justification. Here, the main implication of these arguments is that there might be a way to non arbitrarily show that we need to take certain reasons to be completely self-justifying without requiring that there be a metajustificatory feature which makes those reasons self-justifying. What convinces us we need to take those reasons to be self-justifying need not make them self-justifying. (pg. 544)