It was a decade when black athletes were breaking through in a number of nontraditional sports besides tennis, with Pete Brown and Charlie Sifford winning PGA golf tournaments and Wendell Scott winning a NASCAR race in 1963.
It was widely assumed at the time by all respectable people that Ashe was a harbinger, that men's tennis would continue to become more integrated, that black men would eventually make up 1/8th (but no more) of all professional tennis champions, but that didn't really happen. MaliVai Washington made it to the Wimbledon final in 1996, but there wasn't much follow-up.
Four decades after Ashe, the top African-American male tennis player is James Blake, who is ranked #9 in the world, and is the second best American after Andy Roddick. Blake dropped out of Harvard to play professionally, had some success, but then broke his neck a few years ago crashing into a net-post. He's made a heartwarming recovery.
As you might guess, Blake's mother is white.
African-American women have done better in tennis, but the pattern with African-American males who, unlike Blake, don't have a non-black parent seems to have become that they will either dominate a sport (basketball and football) or not play it seriously. This would have come as a shock to Civil Rights-era white liberals, but there doesn't seem to be a stable midpoint anymore where African-American men will long accept being a minority in an integrated sport.
This wasn't true in the past. For example, in golf, five different blacks won 23 PGA tournaments from 1964-1986 (an average of one per year, or a little over 2% of all tournaments), and these first couple of generations of black touring pros continued to be a small but solid presence on the Senior (Champions) Tour for years more. Since 1986, though, Tiger Woods is the only African-American to make even a splash on the PGA tour, and he's more a representative of this new mulatto elite that makes up an increasing share of African-American participation in white-dominated fields than of the general African-American community.