Ironmills steps will remain closed until further notice.
A landslip next to the path has become substantially worse.
Midlothian Council is to investigate the cause of the further slippage and determine what repairs are required.
The steps, which closed in the spring, are the main pedestrian access from Cemetery Road to Ironmills Park.
A council spokesman said: “We’d like to apologise for the inconvenience. We had hoped that the landslip was minor and once the ground stabilised a repair could be carried out relatively easily. However, this has not been the case and the area of landslip on the path and next to the path has increased substantially.
“It could therefore be some time before this access route can be opened again.”
Access to the park now is via Old Edinburgh Road then Ironmills Road.