Benjamin Hawan, aged 11, is set for secondary school in August, and the family are considering moving to the mainland with Jamie, aged nine, and Georgia, aged seven.
The Hawans' dilemma illustrates the traditional problem of family life on the small islands. The nearest secondaries are Mallaig High and Lochaber High, and pupils from Rhum have to stay in lodgings in Mallaig or in hostels at Fort William.
At weekends, Lochaber High pupils are forced to stay in other accommodation. Mallaig High currently has just three boarders and so does the Fort William school.
Kate Davidson, Rhum's teacher, commented: "When a child reaches high school age, they have to go away and that often results in families moving. Not every family wants their child taken away at the age of 11 or 12."
Ms Davidson has been on the island for three years, and previously taught on Canna for six. Without a replacement family on the Scottish Natural Heritage-owned island, the school will close. "You just accept that," Ms Davidson says. "You know this when you take the job."
Some 35 people live on what has become a nature reserve, with employment controlled by the Scottish Natural Heritage and the Red Deer Commission. Ms Davidson said it was easy to be romantic about life on the islands but in winter it was particularly isolated. There were only four ferries a week and it was impossible to leave for the weekend and return for work on Monday.
Harry MacKenzie, a spokesman for Highland's education department said the authority had no difficulty in staffing island schools. "You are always looking for someone who is adaptable and who can live in a small community. It's important they can mingle," Mr MacKenzie said.
Canna currently has two pupils and little hope of newcomers. Muck has a healthier seven pupils and Eigg comes out top with nine.
Although Rhum primary is not exactly overcrowded, Ms Davidson maintains she still spends evenings and weekends on school work, given the demands of the 5-14 curriculum and her other role as headteacher.
"You have still got to plan resources for children at three different levels," she adds. "The only thing you save on is the marking."