The three children found dead at their family home all suffered the degenerative condition spinal muscular atrophy – sometimes described as 'floppy baby syndrome', it has been revealed.
Three-year-old twins Ben and Max Clarence and their four-year-old sister Olivia needed specialist care around the clock, according to friends.
The children's bodies were discovered at their home in New Malden, South East London, on Tuesday night.
Their mum, Tania, 42, was taken to hospital and was later arrested. She is currently being questioned by police.
The children's 'devastated' father, Gary, was said to be flying back from South Africa with the couple's eight-year-old daughter.
According to the Telegraph, friends said Olivia's developmental problems were only discovered when she was two, and Mrs Clarence was pregnant with the twins.
A series of tests revealed that the couple carried the disease and their children might not live for more than five years.
Lloyd Marshall, who runs a hotel in Johannesburg set up by the Clarence family, said the children's poor health had put a 'massive, massive strain on them'.
He told the paper: "Gary is a family guy, the kids are his world. His wife is lovely too. As a couple they are a remarkable and special family.
"They were working through it, handling it exceptionally. Gary would never have travelled if there was an indication of a problem."
Mr Marshall described how the couple had noticed that Olivia could not sit up properly while on holiday in South Africa and 'alarm bells began to ring'.
Mr Marshall said they were later 'devastated' by the diagnosis because it meant there was a '50/50' chance the twins would have it. They later learned the children might only live for another two years.
He said: "My understanding was it was a maximum of around five years from when they were diagnosed around two years ago. You suffocate because your muscles can't support you at all.
"It was an incredibly devastating story once they found out the problem, and particularly when the twins had the same condition."
Graphic designer Mrs Clarence, who is still being held in a police station near their New Malden home, had given up work 'more out of choice than duty' to care for the children. The family also had at least one nanny and an au pair helping them day-to-day.
The Daily Mail reports that the children were allegedly smothered in their pyjamas and may have been dead for more than a day before they were discovered.
Neighbours said Ben, Max and Olivia were last seen playing in the garden at the family's £2million home in on Easter Sunday.
Worried friends had been unable to contact Mrs Clarence for 24 hours and called police, who arrived at property at 9pm on Tuesday to find the children dead in their bedrooms.
Their mother was found injured in the bathroom and taken to St George's Hospital, Tooting, south London, and arrested on suspicion of murder after treatment to minor wounds.
A family friend said: "She had to cope with so much, she was a very loving mother."
Shocked neighbours said it was a tragedy and called the family 'really, really lovely people'.
Retired nurse Joy Devis, 86, said the deaths came as a 'huge surprise and shock' and other neighbours said they had last seen the children playing in the front garden on Sunday 'larking about'.
They and other well-wishers created a poignant makeshift memorial to the children outside the house yesterday, leaving teddy bears, bouquets of flowers, pot plants and a child's skipping rope in the driveway – which was guarded by police officers.
A Metropolitan Police spokesman said post-mortem examinations were to be held today (Thursday).
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