  We study the resurgent structures of Wilson loops in refined topological
string theory. We argue that the Borel singularities should be integral
periods, and that the associated Stokes constants are refined Donaldson-Thomas
invariants, just like the free energies, except that the Borel singularities
cannot be local flat coordinates. We also solve the non-perturbative series in
closed form from the holomorphic anomaly equations for the refined Wilson
loops. We illustrate these results with the examples of local P^2 and local P^1
x P^1.
