Paramount Home Club company not honoring their service agreement Atlanta Georgia

I purchased a home warranty from Paramount Home Club covering my appliances, electrical, plumbing, garage and air conditioning units. The contract states that they will repair or replace any covered item that breaks down during the covered period. My air conditioning unit stopped working and I expected them to honor their contract. They said the unit had to be maintained before they would repair or replace it. I had an annual maintenance contract with a licensed air conditioning company who maintained and serviced my units and I sent them the contract proving I satisfied their requirements. They refuse to honor their agreement and I have been without air conditioning in my home fopr over ten days in 90 degree weather.