It is short of cash and insurance companies will no longer cover the hall in Cheyne Way.
Group secretary Sandy Banfield said: "I do not want to admit defeat to vandals but another break-in and we will not be able to do any more repairs.
"I just don't understand why these people do it. There is nothing in the hall of any value, except to the Scouts."
The most recent incident occurred on the afternoon of August 5 when the bars of a new reinforced fence were forced apart and two sets of doors were smashed open.
Once inside the intruders broke off the doors of kitchen cupboards, rifled through filing cabinets and damaged trunks containing scouting equipment.
The alarm was raised when a dog walker noticed the door ajar at 4.30pm and called the police.
An estimated £2,000 worth of damage was caused to the hall, which is used by more than 60 Scouts and Cubs every week, as well as local residents' groups.
On previous occasions vandals have urinated on the hall floor and smashed the alarm system, leaving repair bills of up to £4,000.
The recent airshow provided an opportunity for the Scouts to raise funds but volunteers such as Mrs Banfield are frustrated by the actions of a few individuals.
She said: "I am just fed up with it. We paid £3,000 for a new fence four weeks ago and they've already managed to get through that. What else can we do?"
Mayfield ward councillor Craig Card, the Liberal Democrat group leader and a Cheyne Way resident, said: "There are not a lot of things for children to do within the area and the vandalism always gets worse during the school holidays.
"I know the Scout leader myself and I am very concerned to hear that the group is in danger of closing."
Police who attended the scene have taken items for further testing.
Anyone with information should call Farnborough police on 0845 0454545.
Sandy Banfield is pictured by one of the hall's damaged doors.