Why hasn't Jason skipped at least one grade? He's shown to be capable of the work of higher grades.
Imagine it's not just being academically talented, but also having a sufficient level of maturity... the latter which Jason clearly lacks.
Because, while "book smart", he has absolutely no common sense at all.
Andy is well known for her strict nature concerning media and her children. She forbids them from playing violent video games (not that that stops Jason), and throws fits when they even think about seeing R-Rated movies. So why, then, does she allow her youngest son to read A Song of Ice and Fire, which is full of graphic sex and violence? Is she unaware of the book's content, thinking that all fantasy is like The Lord of the Rings, or does she simply think that books are harmless?
Given her reaction to some of Jason's video games ("Why isn't Donkey Kong wearing any pants?!"), it's entirely possible that Jason has kept the true nature of the series from her, much like when he convinced his dad the the "M" on video games stood for "Mild". She has demonstrated in the past that she has very few overlapping interests with Jason, so it's not likely that she would read the books and is probably unaware that A Game of Thrones is based on them, if she watches that at all.
Not just ASOIF. One strip implied that Peter and Paige rented Pulp Fiction and let Jason and Marcus watch it, and another had Jason working on his website when Marcus came in with a huge stack of South Park VHSs and asked Jason if he wanted them uploaded in any particular order. (Keep in mind that when Peter wanted to watch the same show on the MomVo, it told him "Fat chance. You're going to watch Nova".)