The plans, put forward in summer, were expected to save the council £1m over a two-year period.
A spokesperson for the council told PF: “The council will no longer be pursing the proposals”, which were rejected by Unite the union after a ballot on the move.
The plan was suggested after an audit report found that the authority could run out of money within the next two to three years.
In July, the council’s chief accountant denied the suggestion that the council was close to issuing a section 114 notice.
“We do not know where this money will come from at this stage, and savings will need to be found elsewhere,” the spokesperson told PF.
Under the plans, staff would have had to take two days off between Christmas and New Year for the next two years.
A letter to employees, seen by the BBC, said: “We are still planning for county hall to close over the Christmas week and managers have already been working on what this means for their teams.
“The proposed savings from the unpaid leave proposal have been put into individual service area budget plans for this year and next, which means that budgets will have such reductions built into them”.
An external audit report from July found that only £11.1m of the budgeted £19.5m of savings were delivered in 2017-18.
