The Economist has a good, brief explanation of why restitution remains such a problem:

The process of claiming looted artwork is often opaque, ad-hoc, expensive and uncertain. Different countries follow different rules and there is no international arbitrator to resolve disputes. Ownership records are patchy, so these tussles are trickier than those over bank assets frozen during the war. Only five countries—Austria, Britain, France, Germany and the Netherlands—have set up independent national commissions for handling claims, and practices vary. In Germany the commission cannot force museums to negotiate. In America most museums are private, so the government cannot mandate restitution. Different statutes of limitations dictate claims on private collections, and the rising value of the disputed artworks has raised the stakes for everyone. Big auction houses, such as Christies and Sotheby’s, research the provenance of every work and encourage settlements. But smaller houses mostly defer to the law, which tends to favour current owners. Claimants often must rely on the good will of collectors or institutions.

The Economist explains: How is Nazi-looted art returned? (The Economist)