Cheltenham chairman Paul Baker says the club face the "toughest challenge" they have had to confront for many years after the resignation of Simon Keswick.
Keswick, who works in insurance, hotels and retailing and is worth an estimated �996m, has stepped down as a director to focus on his business commitments.
"Next season the board is going to have to be very astute and prudent in considering our playing budget.
"But we'll continue to do everything we can to stay in League One," said Baker.
"The budget will have to be lower and it will be the toughest challenge we have been engaged in for quite a while.
"Losing Simon is a blow, but we are still viable and few clubs make a profit."
Keswick, 66, who made a big contribution to the building costs of Whaddon Road's Carlsberg Stand, suggested he would consider taking up a role with the Robins again once he had retired.
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