Video report by ITV News Wales & West of England Correspondent Rupert Evelyn
Councillors are set to meet on Wednesday to discuss the mascot, which originated on a railway poster, with the caption "Skegness is so bracing".
Health and safety concerns are thought to have cast doubt on the future of the costume, with official documents from the local authority stating: "the costumes have been well worn, are very dirty and will need specialist cleaning before they can be worn again."
But the council has said it has "no provision to store" the costume, it is currently being kept in the Mayor's parlour until a more suitable home can be found.
The council has also cited difficulty finding volunteers for the costume, alongside 20 minute restrictions on the length of time a person can spend inside it, and the need for the costume operator to have a background check if working around children.
One woman, who works at a local hotel but didn't want to be named, told ITV News: "The town isn't losing its mascot as we'll still have the statue by the clock town and station.
"I think it's sad for the town to lose the costume - what if KFC didn't have the bloke dressed up in the chicken outside?
"I don't understand why the BID took it on and now don't want."
Councillors are set to make a decision on the mascot at a meeting on Wednesday evening.
In a statement, spokesperson said: "Skegness Town Council’s discussion tonight is whether the Town Council should store the costume and operate the character," adding it would issue an update once a decision has been made on its future.