The firm continued until 1957, publishing such titles as Who Goes There? (1948) by John W. Campbell, Jr.; The Man Who Sold the Moon (1950) by Robert A. Heinlein; Sidewise in Time (1950) by Murray Leinster [Will F. Jenkins]; The Demolished Man (1953) by Alfred Bester; Science Fiction Carnival (1953), edited by Fredric Brown and Mack Reynolds; and Empire of the Atom (1957) by A. E. van Vogt.
The firm also announced several books it never published, some of which were original titles that were never published anywhere. It was in financial difficulties by 1953, though it managed to publish several more books before going out of business finally in 1957.
For more, see http://www.sf-encyclopedia.com/entry/shasta_publishers