Sage House residential home on St Mary’s may be forced to close after the council withdrew financial help.
The move could mean about 12 people at the home would have to find somewhere else to live.
The facility has been under threat for several years because of a large drop in resident numbers.
The council hoped the situation would resolve itself and has been working with owner Sabina Shrowdolph in an attempt to keep it running.
But it has now decided it can offer no more support.
Protesters fear the possible closure of the home would mean elderly people may have to go to the mainland to retire.
Spokeswoman Marion Bennett said the council could not charge island tax payers more to continue funding the home.