Councillors have agreed to appoint an independent consultant to oversee a new consultation with the disabled users of the Kemback Street centre and their families.
But an attempt by the Labour group, supported by other opposition councillors, to have a representative of parents and carers also be involved in that process was rejected by the SNP administration by 15 votes to 13.
Social work and health convener Ken Lynn insisted the consultation would be taken seriously and said the fact the social work director had recommended the centre be closed did not mean it was a done deal.
He said the Care Inspectorate, which upheld a complaint about the first consultation exercise, had made an unannounced visit to Kemback Street and it was satisfied the centre was operating well.
The council has promised not to go ahead with its original closure plans at least until the outcome of the talks with service users and their families is known.
The job of the independent consultant will be to ensure the talks are carried out properly.
Councillors heard from Moira Leck, who was speaking on behalf of parents.
She said they remained concerned that the social work department was not as willing to listen to their views as they would like.
Mr Lynn said: “We want to validate the process we want service users to have absolute confidence in the process.”
The social work and health committee also heard that an action plan was in place to make improvements to the social care response team, which was criticised in a Care Inspectorate report for the length of time it took to respond to alerts from elderly residents, including people who had fallen at home.
Labour’s Helen Wright said there had been “serious failings”, including a shortage of staff.
Mr Lynn said raw data showed response times had been getting better and he promised that a progress report would come back to committee in six months.