The group's present Scout leader Sue Scott suffers from pericarditis (inflammation of the fibrous sack surrounding the heart), which she contracted after getting swine flu last year.
"As a result, I'm unable to continue the role.
"We've got seven enthusiastic scouts without a leader.
"And we've got more kids who want to come up from Cubs, but we can't take them because there's no leadership."
The Keas and Cubs groups would continue as usual in Fairfield, she said.
The group had investigated sending their scouts to the nearby Mosgiel and Green Island Scout groups.
The problem was both groups already had waiting lists for children wanting to join, she said.
"Fairfield is about 40 years old and we're going to have to close it at the end of this term if a leader can't be found.
"My health means I can't continue. It would be terribly sad if the club had to close - it's been here so long.
"It would break my heart - even more than it already is."
Ms Scott said the group was looking for someone who enjoyed working with children aged between 10 and 14.
It was not necessary to have Scouting experience.
"All they will need is a love of the outdoors, and we'll give them training for the rest."
The Scout group meets on Tuesday nights at the Flower St Scout Hall.
