Coun Kerri Harold and her husband Roy put up the shed, with gravel hardstanding, in a paddock on Ferry Lane, Woodmansey.
Following complaints from neighbours, East Riding Council issued an enforcement notice last July, ordering them to stop using it for functions and events and to remove the shed, and everything from barbecue equipment to planters.
The couple appealed but their appeal was dismissed by a planning inspector in March.
They should have removed everything by June 27, but the day before, put in for planning permission saying the shed was needed for storing equipment to maintain the land.
Coun Harold, who represents Minster and Woodmansey wards, said it had been used to host 18th and 21st birthday parties for her daughters.
She added: “It’s clear the neighbours don’t want anything at all in that paddock. We have nowhere else to store the equipment we need to maintain the paddock.”
Officers are recommending refusal of the application at a meeting on August 7.
An officer's report states there is “currently no bona fide agricultural activity being carried out on the land” and allowing it to stay “could facilitate further breaches of planning control.”
Neighbours are also objecting. One said yesterday: "Everything should have gone by June 27. I feel the council has let us down.
"To put in for planning permission for agricultural purposes is ludicrous. They have no agricultural background."
He claimed the shed contained a disco and wood-burning stove, adding: "They want to continue with these functions and that's why they want it there."
The council alleged a number of breaches of planning controls last year when they issued the enforcement notice last year.
The notice said the erection of the building and "unrestricted storage of goods and chattels" and "functions and events" raised concerns of noise and disturbance to neighbours.