Tourists are being asked to only touch Greyfriars Bobby's nose "gently" after work to restore the statue failed again.
Edinburgh city council officials said damage was still being done following a £400 worth of restoration work to fix the dog's nose.
The statue is popular with tourists, many of whom have taken to rubbing the Skye Terrier's nose for luck.
The local authority said it had no plans to redo the work soon.
Richard Lewis, Edinburgh city council's culture and sport convener, said: "The council arranged for work to be carried out to fix Bobby's nose 12 months ago, but damage is still being done and the restoration is already wearing off.
"In time, we will organise repair work again to maintain the statue, which we know is one of Edinburgh's most loved monuments, but there are no plans to carry out more work out in the near future.
"If people do feel obliged to rub Bobby's nose could we encourage them to do it gently, as it really does cause damage."
The real Bobby was the pet of Edinburgh constable John Grey, who died of tuberculosis in 1858.
Bobby was said to have stayed close to where his master was buried.
The dog's period of mourning reputedly lasted until his own death in 1872.
However, a historian at Cardiff University believes he has uncovered evidence that the story is not true.
Dr Jan Bondeson said there were distinct differences in photos and paintings of Bobby which fell into two groups - those before 1867 and those after.