UnitingCare West started running its Family Foundations Service in November on a three-month trial.
Funding for the program, which costs $35,000 a month to run, was sourced through fundraising and the charity.
The program has so far helped 30 families at risk of homelessness.
But chief executive Sue Ash said without more funding from government or private sources, the program would be forced to close.
‘We are hopeful that applications to a government agency and private sources will come through,’ she said.
‘We think there are still families who we haven’t reached yet.’
Ms Ash said increased demand on support services meant that families were now facing homelessness.
‘Historically, most people who face homelessness are single people,’ she said.
‘Support systems in the community are usually able to meet the urgent accommodation needs of families, mostly because children are involved.
‘But these days, those backstop services are chock-a-block full.’
Ms Ash said this need prompted the charity to start offering support services to families.
‘We made the decision that, while it is best to provide a home for families, we weren’t going to do nothing,’ she said.
‘The service provides a safe environment where children and parents can come and get basic support needs like a meal, shower and a safe place for children to play.
‘It doesn’t take away the uncertainty and the risk of living homeless, but it does mean there is support and from our point of view, we are also able to hook people up to other services.’