Mick Gaffney set up Musketeer Leisure seven years ago and says he has lost £55,000 on the venture.
The company has made no profit for 18 months and is now unable to pay its debts.
Musketeer Leisure took over the skate park at the waterfront three years ago, but that has now also been closed.
Mr Gaffney, who is a public rank taxi driver, feels he has been left hanging by the Waterfront Enterprise Board, who manage the land, since the trampolines opened seven years ago because he was only ever given a one-month rolling contract.
He never put up the £1 price for using the trampolines.
