Steve Fishman and concluded that there are two possible scenarios:
Scenario #1: The American organization acquired copyright under work for hire rules. If the American organization commissioned the painting, it may be considered as a work for hire under the old copyright act (1909 Act). That act was a lot less friendly to independent contractors than the current law (1976 Act) and works were often ruled to be "made for hire" simply because they were created at the hiring party's "instance and expense." (Alternatively, there may have been a written agreement in which the artist transferred copyright to the organization.) In either of those cases, the American organization would have acquired copyright. If it was not timely renewed, it would have fallen into the public domain (assuming the painting was published with copyright notice and the work was registered).
Was the painting published? If the painting was never published, the copyright might still exist. Unpublished works that are "made for hire" are protected for 120 years from creation. A painting is published when copies are distributed to the public, or when the work is offered for sale to the general public, or when the painting is publicly displayed with no restriction on copying or photographing the work. There is no publication if the painting was never offered for sale and was displayed with restrictions on copying.
Scenario #2: Spanish painter retains copyright as a Spanish national. Under this scenario, the American organization did not acquire copyright under work made for hire rules -- perhaps because the arrangement did not meet legal requirements -- and the Spanish painter retained copyright. (BTW, it shouldn't matter where the work was completed.) As a Spanish national, the painter's rights would originate under Spanish copyright laws, and ultimately would receive protection in the U.S. as a result of copyright treaties, most notably the Berne Convention. Under this scenario, even if the painter's agents had registered the work in the U.S. and it had fallen into the public domain due to a failure to renew, the copyright could be restored under the GATT treaty and the Spanish artist would retain copyright most likely for a term of life plus 70 years.