His supporting parts in many of his more notable movies were not big enough, other actors in the same film as he that were nominated for Supporting Actor had bigger roles, for example:
Thomas Mitchell in "Gone With the Wind",
Walter Brennan in "Sergeant York",
Sydney Greenstreet in "The Maltese Falcon",
Jose Ferrer in "Joan of Arc",
Victor McLaglen in "The Quiet Man",
Jack Lemmon in "Mr. Roberts", etc.
He was rarely the 2nd lead, and sometimes not even the 3rd.
Also, from biographies I've read, Bond was somewhat arrogant and crude, staunchly conservative and misogynistic. It's possible his brutish behavior off-screen might have affected his popularity with voting members.