  Let k be a field of characteristic p>0. A theorem of de Jong shows that
morphisms of modules over W(k)[[t]] with Frobenius and connection structure
descend from the completion of W(k)((t)). A careful reading of de Jong's proof
suggests the possibility that an analogous theorem holds for modules with only
a Frobenius structure. We show that this analogue holds in one weak formulation
and fails in a second stronger formulation.
