It appears that he died sometime between the compiling of the 1931 and 1932 New Haven City directories, see the attached. In the 1932 one, Cecelia M. Schultz is listed as widow of Anthony E.
Further evidence of his death in this time frame is that he is named as one of the surviving children in his father John's 1927 obituary but he is not named in his mother's obituary. Regina Schultz's 1932 obituary image is poor but you can figure out from census and directories that the only surviving children named were Otto A. of New Britain, Bernard A. of Meriden, and Mrs Louis Zemke of New Haven.
Also... in case you don't have them, found these vitals.
Connecticut marriage record index:
ANTHONY SCHULTZ and CECELIA TRAYNOR, married 1917-10-23, MERIDEN
LOUIS ZEMKE and MARY SCHULTZ, married 1911-07-03, MERIDEN
Connecticut death record index:
REGINA SCHULTZ, 1932-04-16, MERIDEN
JOHN SCHULTZ, 1927-10-23, MERIDEN
MARY ZEMKE, 1961-04-29, NEW HAVEN
CECEL SCHULTZ, 1958-03-31,NEW HAVEN