If this is successful the original naming rights sponsor, the Perry Group, would change its deal and provide some money upfront.
In a letter to the council, Home of Cycling Trust chief executive Geoff Balme said the challenge had been convincing the Lottery Grants Board the project had national significance and was more than an elite cycling track.
The council's rates control team - councillors Russ Rimmington, Theresa Stark, Tony Armstrong and Jane Hennebry - lost their argument that there were too many holes in the deed.
They supported Mr Rimmington's call for the agreement to be put on hold until they received the next funding update in February. Ms Stark said the deed didn't safeguard the public.
Mr Rimmington doubted any new funding would be secured by the February update. He said the trust hadn't raised a "single cracker" since September and it was becoming clear the money wasn't there.
The council's finance group manager, Mike Garrett, said the deed included provisions which allowed the council to pull out of the deal if its requirements were not met.
The council was reassured its $6 million donation would not change, regardless of whether the trust achieved charitable trust status.