Ministers ignored warnings from officials about the state of Kids Company’s finances on six occasions, according to a report from the National Audit Office.
It says that the NAO observed a "consistent pattern of behaviour" when Kids Company approached the end of a grant term.
On each occasion, according to the NAO, the charity would lobby the government for a new funding commitment.
"If officials resisted, the charity would write to ministers expressing fears of redundancies and the impact of service closures," it says. Kids Company would also express the same concerns to the media, according to the NAO.
"Officials repeatedly expressed concerns about Kids Company, but the government continued to respond to the charity’s requests for funding," the report says.
"As far back as 2002, government records show officials were concerned about the charity’s cash flow and financial sustainability. Officials also noted at that time that other organisations appeared to offer better value for money.
"Briefings to ministers in 2002, 2005, 2007, 2010, 2012 and 2015 show that officials accepted Kids Company’s assertions that it would become insolvent without government grant funding."
It says that officials in the Department for Education expressed concerns about the charity in 2002, when the Home Office was coordinating a cross-government rescue package to prevent the charity going bankrupt.
The DfE said at the time that the charity was not well regarded at local level, that the funding package could set on "unhelpful precedent" and that there were other local organisations that could offer better value for money.
Despite this, Kids Company was awarded £300,000 in emergency funding.
The report says that the charity received £42m in grants from central government between 2000 and 2015, and a further £4m from other public sector sources, including local authorities and lottery bodies, over the same period.
It also says that in February 2013, the DfE, which provided £28m of the £42m that came from central government sources since 2000, prepared a public interest case to support the continued funding of the charity despite its failure to win grants through a competitive process.
Reasons for its continued funding included precedent, because the DfE had funded the charity since 2005, and "reputational damage to the government’s wider agenda" if it withdrew funding.
The charity chief executives body Acevo said in a statement that the report raised serious questions for the Cabinet Office.
"The NAO report clearly demonstrates that the current Cabinet Office leadership allowed a lapse of proper oversight and scrutiny of the Kids Company," it said.
"Under this government, it appears as though Kids Company had a blank cheque and carte blanche. Other charities, many of them operating in the same field with an historic track record, had to scrabble for the crumbs that remained beneath the table while enduring persistent criticism of their activity and intent."
Acevo’s statement also said there appeared to have been "no appetite among the current leadership of the Cabinet Office or the Office for Civil Society to engage with Kids Company's lack of reserves, governance and chronic cash flow difficulties".
It said: "Attention to these are essential to deliver value for the taxpayer while ensuring vital government grants are used in a responsible way.
"Unless the Cabinet Office gets a grip and conceives and delivers a mature and coherent approach to charities, their governance, their reserves and a centrally supported drive towards best practice then many other charities are almost certain to go under."
Karl Wilding, director of public policy at the National Council for Voluntary Organisations, said the report showed that Kids Company was "an anomaly among charities".
He said: "The majority of charities are well-governed and take their sustainability seriously. "Despite its significant income, Kids Company chose not to build up financial reserves in the way responsible charities do in order to see them through lean times."
Responding to the report, a government spokeswoman said: "Since 2002, successive governments have provided financial assistance to the charity to help it deliver services for vulnerable young people.
"The welfare of the young people has always and continues to be our top priority, and we will continue to work with local authorities, charities and youth clubs in Lambeth, Southwark, Camden and Bristol to support young people with the services they need."