Councillors have agreed to pump almost £600,000 more into the restored Brighton Dome complex after sums for running costs failed to add up.
But they have ordered a scrutiny inquiry into what went wrong with the over-optimistic financial forecasting.
Liberal Democrat group leader Paul Elgood told Brighton and Hove City Council's policy committee: "The council played a key role in the Dome restoration project.
"Scrutiny needs to be given into why the costs have overrun so much and how the council monitored its involvement."
The inquiry decision was taken against the wishes of the Labour administration, which does not have a majority on the committee.
Deputy council leader Sue John said the Dome was still in the early stages of its new life and added: "We are all learning.
"Income has exceeded expectations in the first two festivals since then and the prospects are bright."
Tory finance spokesman Garry Peltzer Dunn also called for an inquiry into what went wrong.
He said: "A full explanation is needed."
Opposition leader Brian Oxley said: "We support the extra cash because it is vital the Dome carries on but we are rapidly coming to the end of our patience."
Green convenor Keith Taylor said with the council already facing a financial crisis it could ill afford to put another £600,000 into the Dome.
Cash will go to Brighton Festival, which runs the Dome, and will be conditional on reviews of staffing structures, bar and catering arrangements and income targets.
The council's decision means the Arts Council will also pump more money into the Dome, which will help to secure its future.
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