Listed below are the relevant sections of the Statistical Abstract volumes:
1893 to 1895: Militia
1896 to 1904: Army and Militia
1905, 1906: Miscellaneous
1907 to 1908: Army, Navy,and Pensions
1909 to 1912: Civil Service, Army, Navy...
1913 to 1938: Army, Navy...
1939 to 1944-45: Military and Civil Service(s)...
1946 to 1963: Military Services and Veterans Affairs
1964 to 2004/2005: National Defense and Veterans Affairs
2006 to present: National Security and Veterans Affairs
"Introduction to Veteran Statistics from the U.S. Census Bureau", a 2015 presentation by Nesreen Khashan, U.S. Census Bureau Data Dissemination Specialist. This presentation outlines the U.S. Census Bureau survey questions related to veterans and recommended ways to access the data. It also lists veterans data that is not available from the U.S. Census Bureau, which can save researchers time.
U.S. Census Bureau surveys that ask questions regarding veterans status:
American Community Survey (ACS)
The ACS is a nationwide survey of about 3 million household addresses designed to provide critical economic, social, demographic, and housing information to this country’s communities every year.
Current Population Survey (CPS)
The CPS is a monthly survey of about 50,000 households conducted by the Bureau of the Census, it is the primary source of information on the labor force characteristics of the U.S. population.
Survey of Business Owners: Veteran Business Owners and Veteran-Owned Businesses
The Survey of Business Owners (SBO) provides the only comprehensive, regularly collected source of information on selected economic and demographic characteristics for businesses and business owners by gender, ethnicity, and race.
Survey of Income and Program Participation (SIPP)
The SIPP provides national-level data that collects the source and amount of income, labor force information, program participation and eligibility data, and general demographic characteristics to measure the effectiveness of existing federal, state, and local programs.
U.S. Census Bureau resource for data extraction:DataCensus.gov
DataCensus.gov contains data in the form of maps, tables, and reports from a variety of Census Bureau sources including the decennial census and the ACS.