Frederick William Adolphus Skae was born at Edinburgh, Scotland, on 14 May 1842, the son of David Skae and his wife, Sarah Malcolm Macpherson. His father was the physician superintendent of the Royal Edinburgh Asylum and was well known as a humane psychiatric doctor. Frederick studied medicine in Edinburgh and graduated MD at the University of St Andrews. In 1864–65 he was president of the Royal Medical Society of Edinburgh. He became a licentiate of the Royal College of Surgeons of Edinburgh in 1865, and a fellow in 1868. On 17 May 1866 he married Henrietta Annie Traill in Edinburgh. They were to have at least nine children. At that time Frederick Skae was working as an assistant to his father. In 1869 he was appointed medical superintendent of the Stirling District Asylum in Larbert.
In 1871 a New Zealand parliamentary select committee reported on the administration and cost of lunatic asylums in the colony, which had been the cause of political controversy. It recommended that a British medical practitioner 'having special knowledge and experience in the treatment of the insane' be appointed to 'have the supervision and control of all the Lunatic Asylums in the Colony.' No action was taken until 1875, when former premier Julius Vogel, in London to raise a loan for public works, sought the assistance of the commissioners in lunacy. Subsequently, on 10 May 1876 Frederick Skae was appointed inspector of lunatic asylums in New Zealand. He arrived at Wellington with his family in November.
Skae visited the eight asylums in the country and was generally appalled by what he found. They were grossly overcrowded, and he trenchantly criticised all except the Hokitika Lunatic Asylum at Seaview, to which he gave restrained praise. Of the Sunnyside Lunatic Asylum at Christchurch, for example, he observed that the male department 'is an old, badly-constructed, fast-decaying and already dangerously-rotten building'. In his first report in 1877 he calculated that there was satisfactory accommodation for only 270 of the 783 patients throughout the country. He also identified much wasteful expenditure due to laxity in administration. In response to Skae's recommendations some building was initiated, and he was responsible for improving the efficiency of asylum administration and greatly reducing waste. But the government would not provide the funds for the major programme of expansion and rebuilding he advised. The British Medical Journal observed in 1878 that 'it is certain that the Government will dole out as little as it possibly can, and that the overcrowding and filth and large amount of disease will long continue.'
On 3 March 1880 Skae was appointed inspector of hospitals and charitable institutions, in addition to his previous position. Since the abolition of provincial government in 1876 the public hospitals had been an unwanted burden on central government. Skae was to hold this position for only one year, however, and there is little evidence that he took much action in this area. He was a dedicated psychiatrist and his interest lay primarily in psychiatric health. However, his career was to come to a premature end.
In 1881 a royal commission was appointed to investigate the administration of the Mount View Lunatic Asylum in Wellington after charges of violence towards patients were laid against the lay superintendent, J. H. Whitelaw. Although Skae was in favour of experienced medical superintendents he had supported Whitelaw's appointment, and when the commission upheld the charges he was held to be morally responsible. He was strongly attacked by the press. His criticism of asylum conditions and demands for further expenditure had also made him many political enemies.
In his efforts to improve the physical environment for patients Skae had given little attention to methods and standards of treatment. He also believed that most psychiatric patients were incurable, and under his control psychiatric care in New Zealand's asylums was largely custodial. He was strongly opposed to physical restraint for psychiatric patients, yet he had tolerated its use in the totally inadequate conditions of the Wellington asylum 'to an unusual extent, and more than appeared to me necessary', he stated in his final report dated 15 May 1881.
On 20 May 1881 Skae was given six months' notice of termination of his employment. A month later, on 25 June, he died at his home in Karori, Wellington, aged 39. The causes of death were certified as mental shock and erysipelas of the face. Henrietta Skae subsequently returned to Scotland with her family.