This came after the party received a response to a letter it wrote to the Public Service Commission (PSC) in 2007 about Mosana's alleged irregular behaviour and "incompetence", DA spokesperson Mike Waters said.
"It took the PSC three years to respond to the letter ... it reveals that the investigation by the PSC into Mosana has been completed but that Eastern Cape health MEC Phumulo Masualle has done nothing with it. The MEC, in other words, has stalled the investigation by simply sitting on the PSC report."
Waters said the PSC's reply said that due to the need for further legal guidance it could not make its findings public.
"In essence, the report will remain a secret," he said.
About three years ago South Africans were shocked by a Daily Dispatch exposé of the appalling conditions at the hospital, where it was uncovered that hundreds of newborn babies were dying every year. It led to the dismissal of then deputy health minister Nozizwe Madlala-Routledge.
She had declared the situation at Frere Hospital "a national emergency".
Waters said no action had been taken against Mosana, a former ANC councillor, whom he claimed had no medical or managerial qualifications.
"Why is it that the individual most intimately involved in attempts to cover up the Frere debacle has still not been the subject of any sanctions? He was shielded from any punishment."
Waters asked how the public could be certain that MEC Masualle was following the recommendations of the investigation sice they did not know its findings.
Masualle's spokesperson, Sizwe Kupelo, said it was malicious and mischievous for the DA to accuse the MEC of not acting on the report because the department had received it less than a week ago.
"It has recommendations that we are already working on. The PSC has also given us time frames to report back to them. We will not report to the DA," Kupelo said.
He said the department would not "entertain" any calls to make the report public.
"Ours is to act on its recommendation, not to publish it."