Protesters met with placards and delivered speeches outside the Town Hall ahead of Sheffield City Council's crunch budget meeting to decide the fate of Hurlfield View.
The centre in Gleadless, which provides respite for carers and emergency beds for people living with dementia, is set to close next month.
However, protesters decided to meet outside the Town Hall earlier this afternoon to raise their concerns at the decision as councillors prepared to debate the issue at the budget meeting.
Campaigner Sue Harding was one of the protesters to speak at the meeting and stressed the council would end up spending more money than they would save by closing the centre.
She said: "I understand that they need £3000 and that's all. It's not a lot, not in the grand scheme of things.
"The service users who are using it are going to cost the council an awful lot more money if they have to go into permanent care if they can't get respite.
"It's dangerous to move some of the people we are talking about. it causes them distress, they're used to this place and they are used to their carers. Moving them will cause great distress.
"The centre also has a team of trained staff who know how to handle these people with these types of difficulties around dementia. They will find themselves out of a job if the centre closes."
The council's decision has proved hugely unpopular for families who use Hurlfied View and the issue has also been raised in the House of Commons by Sheffield Heeley MP Louise Haigh.
Campaigners have warned that the closure of the centre will result in a loss of expert staff as well as 20 beds, increasing Sheffield's £900m problem of bed blocking.
A motion to suspend the closure and discuss the proposals at cabinet on Wednesday, February 1, was voted down 48 to 32 confirming the Hurlfield View will close as planned.
Dozens of campaigners braved the rain to listen to speeches outside the Town Hall including from Ms Harding who stressed the importance of good dementia care.
She said: "I'm here to make a plea to those people who have the power and the money to take a compassionate decision around Hurlfield View and stop the closure.
"The measure of a civilised society is how they cares for its most vulnerable citizens. We need to treat these people as the individuals they always were, the individuals they are and the individuals they will always be.
"85 per cent of people arrive at Hurlfield View in crisis either because their care has broken down or the person with dementia has taken a turn for the worse.
"After a relatively short stay there, and thanks to the expertise of staff 85 per cent go back out into the community.
"I hope those people who make this decision can get up in the morning and look at themselves in the mirror and be content that they did a good job."