The care being provided at the centre on Koh Sireh, east of Phuket City, is being questioned in the wake of the mass departure.
In the months since the women and children were captured on a boat off Phuket, there had previously been two escapes from the family shelter on Phuket.
In the first escape, six boys vanished. In the second escape, three more Rohingya disappeared.
About 2am today, all the remaining Rohingya fled the Phuket family centre, with the exception of the sleeping boy.
Officials have declined to provide information but Phuketwan understands that 29 Rohingya women and children had initially been accommodated at the shelter.
With numbers diminished by the first two escapes, the third departure saw all three women and the remaining girls and boys quit the shelter, say reliable sources, except for the boy.
Six of those who fled were rounded up late today near a mosque in Phuket City.
It's not known whether they have been returned to the Koh Sireh shelter or whether there will be changes in security following the mass escape.
Distress and despair are not unusual among would-be refugees who are detained for long periods without clarity about the length of their detention or their future.
It's believed the first ''escapees'' - all of them teenage boys - fled when it was rumored that the Thai government would repatriate the 2000 Rohingya being held in the country to Burma.
The Rohingya are stateless and deprived of their rights in Burma (Myanmar.) Those being held in Thailand after being seized from human trafficking camps or apprehended on boats in the Andaman Sea fear ''certain death'' if they are repatriated.
The Rohingya are being held in small groups at facilities of different sizes throughout Thailand with conditions for them now causing concern.
Television footage shot at the Phang Nga Immigration centre north of Phuket and screened on Britain's Channel 4 showed appallingly cramped conditions, with the muscles of the 276 men likely to atrophy if improvements are not made.
The Rohingya were only supposed to be held for six months.
That time limit, set by the Thai Government, is approaching with no decision yet about the status or the future of the unwanted minority members being held in Thailand.
WHERE boatpeople are kept in inhumane conditions