Let U be a smooth geometrically connected affine curve over Fp with compactification X. Following Dwork and Katz, a p-adic representation ρ of π1(U) corresponds to an etale F-isocrystal. By work of Tsuzuki and Crew an F-isocrystal is overconvergent precisely when ρ has finite monodromy. However, in practice most F-isocrystals arising geometrically are not overconvergent and instead have logarithmic decay at singularities (e.g. characters of the Igusa tower over a modular curve). We give a Galois-theoretic interpretation of these log decay F-isocrystals in terms of asymptotic properties of higher ramification groups.