SDMHA said the impact of the change to referrals had been catastrophic, with only one client referred to the group from the council since December.
Keith Sandle, from SDMHA, said staff would expect to be getting one referral a week and if the situation did not change, they would not be able to continue running the service for more than a few weeks.
“People can come in spend a day with us, we have activities going on all day and a cooked lunch,” he said.
“It really gives the carers that bit of respite as well as our clients getting to socialise.”
Mr Sandle said he could not understand why the council was not telling more people about the day care services on offer.
“We are a vital step before people have to go into care homes or hospital,” he said.
“Our help lets people stay with their families and stay in their homes rather than going somewhere else to be looked after.”
The council said it continued to review how best to work with care organisations.
“[The authority] can only fund providers for the number of social care placements people need but council officers have very recently met with the centre and will continue to work with them to explore ways to attract more self-funded clients, and support long-term sustainability, and help deliver high-quality services that meet the needs of Norfolk residents,” said a spokesperson.