In the first round, Hutchins had posted his first victory since recovering from cancer, and the British duo took the first set against Indian-Pakistani pair Rohan Bopanna and Aisam-ul-Haq Qureshi on Saturday.
They also led by a break early in the deciding set but the seventh seeds hit back strongly to win 4-6 6-3 6-2.
Fleming and Hutchins had finished their first-round match with a run of eight games in a row and they picked up where they left off.
But a poor service game at the start of the second set from Hutchins cost them as Bopanna and Qureshi levelled.
The British pair responded in perfect fashion to lead 2-0 but Fleming was broken to love immediately and they did not win another game.
Fleming and Hutchins will now wait to find out whether they have been selected for Britain's Davis Cup tie against the USA in San Diego.
Captain Leon Smith will name his team on Tuesday for the World Group clash, which begins on January 31.
There was also defeat for Jamie Murray and his Australian partner John Peers, who went down 6-4 6-4 to American Eric Butorac and South Africa's Raven Klaasen.
Murray had been unsure whether he would play the match at all on Thursday after suffering heat stroke following his first-round win.
The Scot required several hours of treatment, with his brother Andy saying: "He wasn't in a great way. We just tried to make sure someone was with him throughout the day."
He recovered sufficiently to continue in the tournament, and would have welcomed the much cooler weather in Melbourne.
But he and Peers were undone by a solid performance from Murray's former partner Butorac and Klaasen in blustery conditions.