FAIRFIELD — Negotiators for the teachers union and the Fairfield-area school system met with a state mediator for the second time in a month on Monday, hoping to end an impasse that has prevented them from signing a new contract.

Among the issues facing negotiators for the SAD 49 Teachers Association and the school district are salary levels, health insurance and teacher preparation time.

Teachers began the year in August without a new labor agreement. The old contract will remain in place until a new one is reached.

Neither representatives from the union nor the school district would discuss the dispute before Monday’s mediation session, which began at 3 p.m. and was scheduled to last well into the night.

In the past, they have said they are hopeful the two sides can reach agreement soon.

“I don’t think we’re at the point where we could not settle this,” Robert Mealey, president of the teachers’ union, told the Bangor Daily News in August.

Negotiations began at the end of March, and the teachers’ association requested a state mediator this summer after the two sides failed to reach agreement. An initial mediation session was held in mid-August.

The two sides faced a similar impasse during contract negotiations three years ago. At that time, an agreement was reached and ratified after about 13 months, the union said.

Neither negotiators for the teachers’ association nor the school district would disclose specifics of the current dispute.

But in general, they said the impasse involves salary levels, health insurance premiums, and the amount of preparation time allotted teachers each day.

“We’ve tried to make sure we’ve given the best we can to our teachers,” Steven Grenier, an SAD 49 board member from Albion, told the NEWS in August.

“We’ve gone further than we said we would to the rest of the board, and we’re waiting for the teachers to say yes,” he said at the time. “We’d like to resolve this and get down to business.”