His death, which is not being treated as suspicious, was reported to British Transport Police in Irvine around 10.40pm on Thursday March 15.
To date officers have made exhaustive enquiries and last month took the unusual step of releasing an image of distinctive jewellery worn by the man in an attempt to identify him.
The image shows a silver Raymond Weil Swiss watch, a gold chain and two gold rings - one with a red stone.
At the time of the incident the man was wearing grey/blue trousers, a light coloured shirt with blue stripes, a dark jacket and black shoes.
Detective Constable David Merchant, the officer in charge of the enquiry, has extended their appeal for information.
He said: "I am really saddened and disappointed that after a month no-one has contacted us to report a loved one missing.
"If you have any information, no matter how insignificant you think it may be, please come forward to help us identify the man in order that his family can be made aware and his funeral can take place."
British Transport Police can be contacted on 0800 40 50 40.