The departure of Mr Wood and Ms Raffills has left the ticket with just two councillors - Chris Fletcher and Dick Quax. C&R councillor Des Morrison quit the ticket in November last year, saying it was too urban-centric.
C&R - the dominant political group that ran the former Auckland City Council for most of its 74 years - is also facing problems in the Albert-Eden-Roskill ward.
There, the party leader and local ward councillor Christine Fletcher has indicated she does not want C&R's Mark Thomas as her running mate for two seats on council.
Before leaving for the United States last Friday, Mrs Fletcher said on Facebook that she hoped an Albert-Eden-Roskill team member would be her running mate, "hopefully an enthusiastic Nigel Turnbull campaigning beside me".
Mr Turnbull - deputy chairman of the Puketapapa Local Board, one of two boards in the ward - is seeking a ward nomination.
Former C&R president John Slater said it was no secret that Mrs Fletcher's preferred running mate was Mr Turnbull, a well-connected and highly regarded local constable in a very parochial ward.
A source told the Herald that the entire C&R Albert-Eden-Roskill team did not like Mr Thomas and were threatening to walk and set up a new ticket if he was selected.
Mr Thomas is holidaying in Canada referred questions to C&R president Karen Sherry. She said C&R was still going through a "highly contested" selection process in Eden-Albert-Roskill, but would not comment further.
A second source said Mr Thomas had got offside with Mrs Fletcher and others over a change of name in May last year from Citizens & Ratepayers to Communities and Residents - still C&R for short.
The source said Mr Thomas, as campaign strategist, had made a lot of promises about rebranding and relaunching the ticket, but nothing happened.
"It has been a complete organisational failure," the source said.
Ms Raffills said she had not finalised plans about who she would stand for in the Whau ward in October.
She said she was not unhappy with C&R and still agreed with its principles, but had come to know her ward better and to realise opportunities in the city did not depend on political alliances.
Ms Raffills - who chairs the hearings committee - often votes against her colleagues and has become a strong supporter of Mayor Len Brown.