In the context of the PhilPapers survey, 'nonreliabilist foundationalism' likely refers to a form of foundationalism that doesn't hinge on the reliability of the methods or processes leading to a belief. It's a position that allows some beliefs to be self-justified or infallibly justified, forming the basis for all other beliefs.
Now, why would this position be popular among epistemologists? Well, it offers a neat and tidy structure for understanding knowledge and belief. It allows us to sidestep the potentially thorny issue of having to establish the reliability of belief-forming processes, by allowing some beliefs to justify themselves or be infallibly justified.
However, from the perspective of cognitive science or philosophy of mind, this neatness might seem a bit too neat. It seems to ignore the messy, complicated processes that actually occur in our brains when we form beliefs. It's perhaps for this reason that philosophers in these fields are less inclined to embrace nonreliabilist foundationalism.
In the end, the popularity of a philosophical position often has as much to do with trends, historical context, and individual philosophical leanings as it does with the inherent merits or demerits of the position itself