The family of Paul Rosenberg, a renowned Paris art dealer whose gallery had exclusive arrangements with Braque, Matisse and Picasso, has worked tirelessly, with tremendous success, to recover the 400 works the Nazis looted from him.

That Mr. Rosenberg kept meticulous records and purchased museum-quality art helped the family to reclaim all but 60 pieces. The works recovered in recent years include Matisse’s “Woman Seated in an Armchair,” discovered in the Munich apartment of the reclusive Cornelius Gurlitt. Another Matisse, “Woman in a Blue Dress in Front of a Fireplace” was returned by the Henie Onstad Art Center in Norway in 2014.

But one pastel portrait by Edgar Degas, an image of particular importance to Paul Rosenberg, has proved to be maddeningly elusive.

For decades, the family has been tracking the pastel, “Portrait of Mlle. Gabrielle Diot,” created in 1890. Yet efforts to recover it have been repeatedly thwarted, even though the family knows the identity of a German dealer who has tried several times to sell it.