The sculpture sat above the Art Centre's north quad for 30 years and was Dawson's first piece of public art.
Echo was damaged in the 2011 earthquake and taken down.
The Christchurch Art Centre set up a campaign to raise the $30,000 needed to recreate and reinstall the piece.
However, donations have fallen significantly short, with only $4275 raised from 42 donors.
Fundraising manager Suzanne Henson said the shortfall meant the project was on hold
"The reinstatement of Echo won’t go ahead in the foreseeable future because the Arts Centre’s current priority is to complete restoration of all 23 of its heritage buildings."
She was hopeful the project would be revisited.
"We realise Echo is a popular sculpture that is well-loved in Christchurch."
Dawson said: “ I consider it [Echo] my most successful work because of it's complex simplicity and it's fresh accessibility."
Christchurch born Dawson has created several pieces around the city including the Chalice, which was installed in Cathedral Square to mark the new millennium.