Under Fanstone New Zealand doubled that medal return in London, with gold in the women's 470 (Jo Aleh and Polly Powrie) and a silver in the 49er (Peter Burling and Blair Tuke), before doubling it again in Rio this year.
Yachting NZ's haul of one gold (Burling and Tuke), two silver (Aleh and Powrie; Alex Maloney and Molly Meech, 49erFX) and a bronze (Sam Meech, Laser) matched their previous best return at the Barcelona Games in 1992.
Abercrombie said while he disappointed to lose Fanstone, his resignation did not come as a surprise.
"I know how demanding the role is, very few high performance directors do a third cycle. It's a pretty tough job," he said.
"His last comment was it's been hard work and he wants to just reconnect with his family and spend more time with them."
Yachting NZ are one of several national sporting organisations, including Cycling New Zealand and Triathlon New Zealand, on the look-out for new talent to lead its high performance programmes, with there typically being a lot of turnover in these roles at this stage in the Olympic cycle.
Abercrombie said his organisation will advertise for a new high performance manager once the structure of the role has been confirmed.
"We need to have a thorough review of where we want to go. It's given us the opportunity to reevaluate our whole high performance programme and I need to sit down with High Performance Sport and our board and have a discussion around what the structure should look like."