Missouri Death Records
Death certificates for Missouri 1910-1960 deaths can be downloaded and printed out for FREE, at this site:

- - Birth & Death records for Missouri began in 1910 - -

http://www.sos.mo.gov/archives/resources/deathcertificates/#...

It's also possible that the father in question simply "walked away" from the family. Census takers would then mark the wife as a widow.