Edith Cook, an exhibition parachutist from Ipswich, took her first flight in a plane in France in 1910.
Critics said the proposals for a statue of her in the town "overlooked" her role as a balloonist and a parachutist.
But the heritage group which put forward the plans said the sculpture needed to be historically accurate.
Suffolk Heritage Aviation Group (SHAG) said Cook could not be "seated in, for instance, in a Spitfire, or clothed in a recognisable flying jacket, just for 'aesthetic' reasons".
Members of the Ipswich Society had raised objections to the plans, saying the statue needed to be "sufficiently well designed to convey a clear message from a distance".
Born in 1878, Cook applied for a position as lady parachutist when she was 20 and completed hundreds of descents through her career.
She learned how to fly in France and had planned to fly across the Irish Sea but died after a parachute accident in Coventry in 1910, aged 31.
"Her significance in aviation history has been sadly overlooked," SHAG said.
Two years ago the group helped dedicate a headstone on her previously unmarked grave in Coventry.
Andy Taylor from the group said it "still very much intends to continue with the project" to install a statue of Cook "if not in her hometown, then in her home county" after the Fore Street plans were rejected.
The council said there had been full support from all committee members for a statue and it would welcome a revised design.
A proposed statue in memory of Britain's first female pilot has been rejected for being "underwhelming" and not recognisable as an aviator.