Why does a thermostat for an ac unit go dead at the same time that the fire alarm goes off and they are on the same circuit Is it the thermostat that needs to be replaced or what?

That's probably a safety feature. If you have a forced air system it can blow smoke and embers all over the building in a fire, causing health and damage concerns. By disabling the heating system during a fire the furnace will not actively spread the fire. You may want to contact the installer to verify this. What kind of thermostat are we talking about? built-in to a window unit or on the wall for central AC? Is it a residential or commercial system? If a wall mount thermostat, is it with a clock? electronic or mechanical? When you say fire alarm, do you mean a commercial fire alarm or the smoke detectors in your home? If in your home, are they hard wired or battery only?