Dame Elizabeth, a former chairman of the Association of District Councils, and independent Roy Cross were pressed to resign from the CoR by the Local Government International Bureau and the local authority associations after losing their district seats in the May elections.
Mr Cross stepped down, but Dame Elizabeth told LGC this week she had no plans to give way.
Members only have to be elected at the time of appointment, which was in 1993. The present term ends in 1997.
She said the CoR believed 'they could not continue running efficiently if this continued, so I thought 'all right, I'll stay on' '.
The LGIB policy board has withdrawn funding from her. She agreed she should not get any funding, she stressed.