Bury have been given a 35-day extension after a winding-up petition brought by HM Revenue & Customs was adjourned again in the High Court.
The club, expelled from the English Football League in August as a result of financial problems, had been given 14 days on 16 October to pay off debts.
Bury's lawyers told the court a further extension was needed to establish whether the club paid too much tax.
The case was adjourned by Judge Nicholas Briggs until 4 December.
The Shakers had looked to be on the brink of liquidation after a prospective buyer for the club ended their interest earlier in October.
However, the club say they believe they have continued to automatically pay tax on wages that would otherwise have been paid to staff, despite those wages not being paid.
The judge therefore issued the adjournment to "determine whether HMRC have been overpaid".
Bury North MP James Frith previously met with the Football Association to discuss the possibility of the club rejoining the pyramid at National League level.
Meanwhile, a group of Bury supporters have also worked on plans to form a phoenix club and, if successful, would have to apply to the FA for entry into the English non-league pyramid next season.
A statement issued by the group on Wednesday said: "Whilst the fate of The Bury Football Club Ltd continues to officially hang in the balance, the work of the phoenix group and the volunteers involved will continue.
"The town of Bury needs and deserves a football club. It needs a football club that will never find itself in this position ever again.
"We will continue to sow the seeds for a rebirth for when the seemingly inevitable occurs. There will be a football team in Bury come August 2020 and our resolve to see this through remains as strong as ever. "