Numerous repairs have been made to the platform which carries the upper level of the carpark, but problems remain. The car park was built in 1982.
"Various repairs have been undertaken but there is a still an issue with water ingress," an Auckland Transport spokesman said.
New restrictions on the maximum permitted weight on the upper level were introduced in 2014.
"As the weight restriction was not being adhered to, we have recently made the signs more visible to reinforce the need for this weight restriction to be complied with," the spokesman said.
Fines were not being considered, he said.
Desley Simpson, the Auckland Council member for Ōrākei, said on Facebook that the signage related to monitoring of the structure "for seismic weakness".
She said she was still waiting for a definition of SUV, but in the meantime urged people to "think 'Remuera tractor'."
Drive a SUV? Please keep off top level of Clonbern Rd carpark in Remuera
Will update on progress re development of this carpark later
Posted by Desley Simpson on Wednesday, 8 August 2018
The AT spokesman said the carpark structure is being monitored monthly and an assessment of the load it can safely carry was made this year.
"We must make it clear there is no evidence of structural distress and there is no need to close the carpark."
Several people commented on Simpson's post.
One appealed for height barriers to be installed, saying they were "still seeing big Rovers etc up there and if it is a health and safety issue - especially for people in the carpark below - surely the money would be well spent".
Another said, "I have a [sic] SUV, but would not weigh 2000kg. And where will most of Remuera park their Range Rovers etc."