His 4–3 loss in 1983 to Australian Alan Bond's wing-keeled challenger Australia II was the first Cup defender to be defeated in the 132-year history of the race, simultaneously ending a run by the New York Yacht Club that began with the first contest.

Following the loss Conner formed his own syndicate, the Sail America Foundation, through which he raised funds to mount a challenge on behalf of San Diego Yacht Club, culminating with winning the Cup back from Australia in 1987.

Representing San Diego Yacht Club, Conner's Sail America Foundation faced another controversial challenger in 1988, backed by New Zealand banker Michael Fay.

[5] Fay's team abandoned the 12-meter format that had prevailed since the pre-WW II demise of the massive and fantastically expensive J-sloops, and challenged with a huge and unconventional 90' super-sloop (KZ1).

Conner was a rare non-billionaire fielding a team to compete in the 2003 America's Cup, held in New Zealand, receiving funding of up to US$40 million from his sponsors.

Despite raising the boat from 55 feet of water and eventually repairing it, they were unable to recover the valuable testing time lost and they were defeated in the quarter-finals of the Louis Vuitton Cup.