Stockport Council, Cheshire East and Manchester City Council (MCC) are all involved in managing the road.
MCC said most of the road was outside the Manchester boundary.
Stockport Council said on Wednesday that the section of the road from Bramhall junction to Styal Road would remain closed ahead of an anticipated freeze.
A spokesman said: “The disruption to journeys and the knock-on effects it has had are not lost on us and we apologise for any inconvenience caused.
“Our priority is always the safety of drivers and passengers, and while we know these decisions are disruptive, they are made with safety at the forefront.”
Cheshire East Council said the A555’s drainage systems are still recovering from storms which caused flooding in December and the problems are “not straightforward to resolve”.
“They require co-operation from river authorities, utility companies and neighbouring councils to improve the wider network of waterways,” a council spokesperson said.
