In January 2012, Strathclyde Partnership for Transport (SPT) awarded Clydelink a five year contract costing £900,000 to operate the service from Monday to Saturday.
Because of the small number of people using the ferry on a Sunday it was suggested the sailings should be cut.
But SPT members decided the Sunday service should continue for summer 2012, which ran from April 1 until October 14, on a trial basis.
The cost of providing the Sunday service was £16,398, but only 1061 passengers used the ferry, equating to a cost of £15.45 per head.
A report to SPT states: "The reduction in passenger numbers has resulted in the subsidy cost per passenger on Sundays rising from £15.45 in 2012 to £21.60 in 2013, far in excess of what is acceptable.
The report recommends no further subsidy should be provided for the Sunday service to the Rosneath peninsula village, meaning it will be scrapped.