Why were the Keough children were admitted to the Randwick Asylum for Destitute Children?

Annie Nicholson was the third child of Fanny Norman and Henry Nicholls, two convicts who had been transported to Hobart in Van Diemen's Land (Tasmania, Australia); and a younger sister of my Great, Great Grandmother, Louisa Nicholls. 

Note: Some of Anne's siblings were given the "real" surname of her father, Henry Nicholls, and other's had their name given as Nicholson. It seems ex-convicts commonly changed their names to remove the stigma of being a transported criminal.

Anne was born on the 16 March 1858 in Maitland, after her parents had left Tasmania and resettled in New South Wales. In December of 1874, Anne married William Keough aged 18 in Elizabeth Street Sydney, at the residence of James Fullerton L.L.D., a minister in the Presbyterian Church, who was occasionally sanctioned for performing "Quick" marriages.

Four children were born to this couple:

• William Henry Albert George Keogh in 1975
• Florence Annie Matilda Keogh in 1977
• Victoria Ellen May Keogh, aka May in 1880
• Annie Louisa Keogh, aka Louisa in 1882

In September of 1885, three of the children, William, Florence and Victoria were admitted to the Randwick Asylum for Destitute Children by their father, William. The reason recorded by the asylum was that "[Their] Mother deserted. Father cannot look after them" William had to pay 7/6 (7 shillings and 6 pence) for the board of his children.

From the records of the Randwick Asylum of Destitute Children

The children stayed for many years in the Asylum until they were old enough (around 13 years of age) to be "Be Transferred" to wealthy households as servants, having done one years apprenticeship to the Asylum, training for their new duties.

My question however is why the youngest daughter was not sent to the asylum? Did her mother take her with her? Or was it because their mother was very ill? Anne died 8 years later in 1893, aged only 36 of "Chronic Brights Disease", a kidney disease, and described in terms of the day at the link provided.

I have the records, but not necessarily the real reasons or answers. I have a theory that the children were sent to the asylum as Anne was too ill to look after her children, rather than deserting her family, or so I would like to think!

Sources:

• New South Wales, Australia, Registers for the Randwick Asylum for Destitute Children, 1852 - 1915; NSW State Records
• Certificates from the NSW Register of Births Deaths and Marriages held by self