The movie was not nominated for many Academy Awards because of its risqué material, such as the clear themes of alcoholism and prostitution. The subject matter was apparently also the reason that Ginger Rogers wasn't nominated for a Best Actress Oscar (despite a general impression that she should have been). Nonetheless, Rogers did win the Oscar that year, but for a different film -- Kitty Foyle (1940).
This film made a profit of $110,000 (about $2.1M in 2021) for RKO according to studio records.
In the book 'Film Crazy' (by Patrick McGilligan, p.110) while speaking in one of his very last interviews, actor Joel McCrea remarks about 'Primrose Path':
"Actually, that's the picture that Ginger really won the Oscar on; Frank Capra said that. Kitty Foyle wasn't that great in comparison. But they were afraid of the subject matter [of Primrose Path] in those days."
This movie opened at the Biltmore Theater on January 4, 1939 and ran for 166 performances.