In a fiery parliamentary inquiry, Mr Goyder wouldn't answer when asked if his position was untenable, but said he felt assured he had major shareholder support to continue.
The committee is probing what role Qantas played in the transport minister's decision to knock back Qatar Airways' application to double its flights to Australia, but quickly turned to the scandal-embroiled carrier's reputation.
After the Transport Workers' Union, Pilots Association and Australian Shareholders' Association added their names to a number of politicians calling for him to quit, Mr Goyder stuck strong.
While admitting Qantas "has some work to do", he said a meeting with shareholders after Alan Joyce's recent retirement as CEO encouraged him to kick on.
"They want the continuity of leadership of me as chair of the board and particularly with a new CEO," he told the inquiry.
"None of us put our personal interests ahead of (Qantas), so while I retain the confidence of our shareholders and the board, I'll continue to serve because I think we've got some very significant challenges in front of us."
New CEO Vanessa Hudson confirmed the airline had asked the government not to approve Qatar's bid.
"We said the rest of the market should be given a chance to recover before such increases were considered and that is exactly what's happened," she told the inquiry.
Earlier, Qatar said it was "surprised and shocked" when it found its application was rejected through the media, but maintained it could deliver the extra services by Christmas if the government changed its mind.
"We had plans to deploy those aircrafts well in advance, we have to make sure ... aircrafts are aligned," senior vice-president Matt Raos told the hearing.
"We aim to operate before Christmas, we hope we manage to do that."
Coalition senator Simon Birimingham said that "would be great news for travellers and our tourism sector".
Qatar estimated the additional flights would add $3 billion of economic benefits to Australia, adding the Victorian government was predicting a second daily flight from Doha to Melbourne would create 900 jobs.
Australian Airports Association CEO James Goodwin agreed a review into the Qatar rejection was necessary because it wasn't in the national interest.
"We should be putting the red carpet out for any carrier that wants to fly into and out of Australia," he told the inquiry.
"More flights means more jobs, it's as simple as that"
Qatar has 28 flights, compared to Emirates' 84 weekly flights and Etihad's 63.
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