The National Missing Persons Helpline will close unless it can find £500,000 before the end of this month.
A shortfall in funding means the charity needs a cash injection to avoid insolvency.
NMPH spokesman Graham Sefton said the organisation was "a victim of its own success", as funding had not risen in line with demand for its helpline.
"Many people believe that the NMPH is or should be government-funded, so they are reluctant to give anything," he said.
Sefton said that the shortfall was partly due to a drop in public donations since the Asian tsunami appeal.
The charity receives no core state funding. Instead, it relies on lottery grants and corporate and public donations to provide the majority of its annual budget of £4.1m.
Sefton said: "We have every confidence the Government will recognise the need to keep the NMPH running."