The Kresge Foundation, which supports organisations contributing to "the wellbeing of mankind", has given $2m (£1m) to the centre's building programme.
For the past three years, the centre's auditor has included a note in the charity's annual accounts evaluating its financial viability as a direct result of refurbishment costs.
In November 2007, auditor John Bourn, who is former comptroller and auditor general, wrote that only 95 per cent of the building cost was accounted for, and that further fundraising was under way for the remaining 5 per cent.
His note said the charity's financial uncertainties could cast "significant doubt about the entity's ability to continue as a going concern".
Bourn also warned that a £4.6m pensions deficit and loan facilities that are due to expire in June this year could cause potential problems. The charity's reserves, which stood at £2.3m when the report was published, were intended to form a buffer against further deficit in the 2007/08 financial year.
A spokesman for the Southbank Centre said: "We always said publicly that the reserves would be invested in the Royal Festival Hall reopening and we are still expecting results to be in line with projections. The auditors were taking a specific point in time and their going concern issues centred around the claim from our contractors, which has now been satisfactorily resolved."
There were additional grants to the centre from the Weston family and the Clore Duffield Foundation.