Around 40 part-time community education tutors, aged between 65 and 83, were told in January they were being dismissed because the council's employment policies favoured younger staff.
But protests have forced a temporary reprieve. The city has withdrawn the dismissal notices and is to conduct a review of its employment guidelines.
Hundreds of mainly elderly students could have lost their day-time classes in arts and crafts, upholstery and ballroom dancing without the reversal.
Elizabeth Wardlaw, a Liberal Democrat councillor, who admits to being over 60, said: "If we are going to have lifelong learning, then this group of students can have it and the tutor group can give it."
Elfida Nelson, aged 70, a part-time art tutor in Leith, said colleagues were "very upset" when they received letters of dismissal.
The council had a longstanding policy on employment rules but had never used it until now. There was no basis either in European law for removing people over 65, an argument some officials had deployed, Mrs Nelson said.
With the Prime Minister backing the contribution of older people in the workforce, it was crucial the city continued to employ tutors with skills to offer.
"What young ambitious teacher would want 120 hours a year? It's a piece of nonsense. I can understand the thinking behind this that younger people be employed wherever possible but are there really people out there who would want the jobs?
"This is temporary, pay by the hour, thank you and goodbye," Mrs Nelson said.
She believed that 80 per cent of students were themselves retired and appreciated having a tutor they were comfortable with.
"You build up a repartee over the years," she said.