We give a lower bound on the codimension of a component of the non-abelian Hodge locus within a leaf of the isomonodromy foliation on the relative de Rham moduli space of flat vector bundles on an algebraic curve. The bound follows from a more general bound on the rank of a flat vector bundle for which the Hodge filtration persists through the isomonodromic deformation. We will show how this latter bound can be extended to apply to flat vector bundles that do not underlie a variation of Hodge structures, so that it generalizes a result of Landesman-Litt.