Properly discontinuous actions of a surface group on Rd by affine transformations were shown to exist by Danciger-Gueritaud-Kassel. We show, however, that if the linear part of an affine surface group action is in the Hitchin component, then the affine action is not properly discontinuous. The key case is that of linear part in SO(n, n − 1), so that Rd = Rn,n−1 is the model for flat pseudo-Riemannian geometry of signature (n, n−1). Here, the translational parts determine a deformation of the linear part into SO(n, n) Hitchin representations and the crucial step is to show that such representations are not Anosov in SL(2n, R) with respect to the stabilizer of an n-plane. Joint with Tengren Zhang.