Mr Fyfe (50) announced his intention to leave his job before the end of the year. Some analysts have called for him to leave by the end of the June financial year to give his replacement a chance to take over in a new year and at a time the Government was planning a sell-down of its stake in the airline.
Craigs Investment Partners broker Peter McIntyre said there would be no pressure on Mr Fyfe to leave until he was ready.
"Some will want him to help with a seamless transition through the financial years but others will want him to help with the partial sell-down.
"It's one of those situations that means it will never be the right thing for some people, no matter what happens."
Mr Fyfe joined Air New Zealand in 2003, becoming chief executive in 2005. He started his working career in the Royal New Zealand Air Force in 1979.
Air NZ is set to report its first half results on Friday. Craigs has downgraded its reported profit forecast by 25% to $120 million to reflect November fuel prices, coupled with guidance from the recent investor day.
Air NZ noted fuel and softer international demand - resulting in an inability to pass through the fuel increases - were creating barriers for earnings, although the airline expected an improvement in the full 2012 year, Mr McIntyre said.
Domestic and transtasman routes remained stable and profitable, benefiting from more rational industry structures with the withdrawal of Pacific Blue from domestic jet routes in October 2010 and the Virgin revenue-sharing alliance from July 1 last year.
International routes continued to create earnings "head winds" with subdued demand in Europe due to the weaker backdrop of sovereign debt issues and high fuel prices creating challenges for yield management, he said.
"A review of the international business is under way, targeting $110 million of savings by 2015 although management note there is no silver bullet with the focus on product alignment, network positioning and a leaner cost base."
All those challenges would have to be faced by the new chief executive, along with the further sell-down of the company, Mr McIntyre said.
Mr Fyfe had been there for a long time and was a charismatic leader and good communicator.
His replacement would not be as widely understood.
Most boards would be prepared to let the new chief executive stamp his own mark on the business and the Air NZ board was experienced and functioned well, he said.
The new chief executive would understand Air NZ was the flagship airline for the country and that profitability was the main aim rather than access to global destinations on a daily basis.
As far as any replacement for Air NZ chairman John Palmer was concerned, Mr McIntyre believed there would be a succession plan already in place.
"We would hope that those coming in to that board environment would have broad industry experience in the airline sector. That has to be a given."
Asked what he hoped the new chief executive would achieve for investors, Mr McIntyre said his top pick was getting the share price back to $2.
At 86c, Air NZ was trading close to its Global Financial Crisis low of 72c.
