I know that, when $\mathcal{F}$ is a coherent sheaf on a smooth algebraic variety $X$ over a field $k$ equipped with a connection $$ \nabla: \mathcal{F} \to \mathcal{F} \otimes \Omega^1_X, $$ then $\mathcal{F}$ is automatically locally free.

Does this result remain valid when one has a connection with logarithmic singularities along some normal crossings divisor?

Any reference, examples, counter-examples will be appreciated.