Barrow Borough Council's licensing committee spent three days considering David Gill's request.
But the council refused permission for the extension after inspectors raised concerns about "out-of-date practices".
Karen Brewer, the zoo's chief executive officer, said great strides had been made to improve the zoo and keep it the "unique attraction" it is.
Whoever takes over running the zoo must apply for a new licence within the next six months.
Mr Gill first received a licence to run the zoo in May 1994, when the attraction consisted of 290 animals on 12 acres with about 200 visitors a day.
Now the zoo is home to more than 1,000 animals across 50 acres, attracting more than 250,000 visitors and generating Â£3m a year.
The council has gone along with an inspector's recommendation that the licence, which must be renewed every six years, should not be reissued until new management is in place at the zoo.
A report to the committee said: "Of particular concern to the inspectors is the fact that as this zoo grows, it relies heavily on (Mr Gill's) experience implementing out-of-date practices and refusing to implement modern zoo practices.
"This has resulted in animal welfare issues, a higher than expected mortality rate amongst the animals, higher than expected incidents (such as injuries to the public from animals), and places both staff and the public potentially in danger."
The council said Mr Gill had installed new management but there were concerns about him, as licence holder, overruling other management decisions.
Ms Brewer said: "I am confident in my own position to manage the zoo without David here on a regular basis but we do need his ideas and his contribution in this zoo as it is vital to keep its heart alive."

The 47-year old taxi driver, from Eccles, Salford, was taking aid to Syria when he was kidnapped and killed by Islamic State (IS) militants in October 2014.
At the time, he was the fourth western hostage to be murdered by the group.
People in Eccles laid the ribbons in memory of Mr Henning.
A similar tribute was held in the days after his death.
Meanwhile, Eccles MP Barbara Keeley has renewed calls for Prime Minister David Cameron to officially recognise his charity work with a posthumous award.
"I think there should be some way to mark the noble sacrifice that Alan made," said Ms Keeley.
"His mission to help children in Syria was a remarkable one and, of course, he lost his life.
"I think that should be marked with some sort of formal award."
Ms Keeley said she had spoken to Mr Cameron and hoped there could soon be developments.
Prayers will also be said over the weekend at Eccles Parish Church.

The steps to Petit Port Bay were shut in May after damage caused by heavy rainfall during storms.
An inspection by engineering consultants Frederick Sherrell Ltd will start on Monday and is due to end on 27 March.
The department said if no further work was needed the steps should be re-opened for the Easter holiday.
Four parking spaces will be suspended in the Petit Port car park for the duration of the works.
The bay was previously closed between 2001 and 2005, after a series of landslides made the area too dangerous to access.
It was only reopened after new concrete steps, handrails and fencing to contain rockfalls were installed.
Councillors have refused to renew the licence of the owner and founder of South Lakes Safari Zoo.
[NEXT_CONCEPT]
A Greater Manchester town has been adorned with yellow ribbons to mark the first anniversary of aid worker Alan Henning's murder.
[NEXT_CONCEPT]
Steps at a bay in Guernsey could be opened by Easter, according to the environment department.