The Firs hostel at Bakewell is run by a consortium of five district councils and the county council, but some are ending funding and the remainder do not want to make up the shortfall.
The refuge, used mainly by women and children fleeing violence, is managed by Derbyshire Dales DC. Each of the local authorities contributes £4,500 towards running costs.
However two councils - Chesterfield and Bolsover - say they are withdrawing their support. Erewash BC says it is considering doing the same and two of the remaining members of the local authority consortium are reluctant to pay more to keep the refuge going.
'I think it would be a tragedy for the Firs at Bakewell to be affected by this action'.