Critics led by former great Mark Waugh have questioned Aaron Finch's ability to captain Australia at the Twenty20 World Cup after another failure during their New Zealand tour.

World number two Australia slumped to a 2-0 deficit after the second T20 against the Black Caps in Dunedin on Thursday, leaving them on the brink of a series defeat against a side ranked sixth in the world.

The Australians, comprehensively outplayed in the first match, looked rudderless until a Marcus Stoinis-led fightback left them four runs short of an unlikely victory.

Finch's doubters questioned his leadership credentials and pointed to his ongoing struggles opening the batting, with scores of one and 12 during the series.

"His job is to score runs... no batsman is immune from being dropped when you're not scoring runs, doesn't matter if you're captain or not," Waugh, now a pundit, told Fox Cricket.

Finch, 34, also failed to fire in the recent Big Bash League, averaging just 13.8, and he failed to attract any bids in the Indian Premier League auction.

"Finch is running out of chances to book his ticket to this year's T20 World Cup in India," Sydney Morning Herald cricket writer Andrew Wu said.

The Australian newspaper's Peter Lalor contrasted Finch's 12 runs off 14 balls in Dunedin with Stoinis' 78 from 37 and rookie batsman Josh Philippe's 45 from 32.

"They're both down the order to accommodate Finch; all they really did was show him up," he wrote.

Lalor said Finch's poor run "means he's only being picked right now for being a great captain and fabulous bloke".

Former Australia captain Ian Chappell did not address Finch's role directly but did nominate potential replacements as captain, saying Pat Cummins, Alex Carey and Moises Henriques could all do the job.

"The first thing with Cummins -- and he'd be my first choice -- is he's going to hold his place in the team all the time, and secondly, he's an inspirational cricketer," Chappell told Channel Nine.

"If you can't be inspired by Pat Cummins no one is going to inspire you."

Despite this, Finch received staunch backing from Stoinis, who said his teammates felt the same way, declaring: "We've got his back."

"He's arguably the best T20 batter in the world over a long period of time," he said after the Dunedin match. "His record's so good and he's our captain... in our heads we just trust him."

The third T20 is in Wellington on Wednesday.