Appears in collection : A Conference in Arithmetic Algebraic Geometry in Memory of Jan Nekovář

We generalise a theorem on the existence of Frobenius isocrystal and Fontaine-Laffaille module structures on rigid flat connections to the non-proper setting. The proof is based on a new strategy of a point-set topological flavour, which allows us to produce a purely $p$-adic statement and thereby to avoid complex-analytic methods. Joint with Michael Groechenig.