The paddlers' lawyer, Anna Longdill, argued that the selection for the boat's crew in the World Championships should be brought forward two weeks to June 1.
Ms Longdill said if the team did not compete at the World Championships, their Olympic dream would be over.
The pair had already missed out on qualifying at the World Cup, and bringing the date forward would allow both a fair chance to appeal if they were not selected a second time, she said.
"The difficulty is that if these athletes are going to do well at the World Championships, and they need that if they're going to get to the Olympic Games, they need it now.
"They need support and a coach, they need a national organisation to get behind them. It's in the interest of the sport for everybody to move on."
CRNZ's lawyer, Paul David, said the selection date should not be brought forward.
Justice Matthew Muir declined the interim order, saying it would not be fair to CRNZ's selection process.
"For this court to tell Canoe Racing New Zealand that it has to send a boat to the World Championships is a very tall ask," he said.
After the order was declined, the paddlers indicated they would withdraw from pursuing the order further - but another hearing is still set to go ahead.
Ms Longdill has applied for the matter to be heard at an urgent hearing within a fortnight so Quickenden and Fitzgerald "get their day in court".
CRNZ chief executive Mark Weatherall welcomed the withdrawal of the interim proceedings. However, it was unfortunate the matter was not yet resolved. NZME.
