I have replaced the batteries in both thermostats.

You mean the inside unit and the outside unit both shut off?

When I run the heat for cold nights or the ac for warm days, they shut off after about 1 min.

Ok, is your t-stat programmable? And how do you get them to come back on? Do they do it on there own or do you have to reset it?

Hi They come back on every 15 minutes or so. Yes they are prpgrammable though now it does not appear to be coming back on at all.

OK, can you take your t-stat off the wall?

I can remove the front pannel.
I can remove the thermostat if needed.
I have one updtairs and one down stairs.
What do I need to do?

Do you have more then 1 ac? Or do you have a zoned unit?

If you have a zoned unit you will probably need to call a local hvac contractor

It is one AC - a zoned unit.
I reset both thermostats but nothing came on.

Did you try turning off the power to the main zone box at the furnace?

What brand zone control do you have?

They are white-rodgers model 1F80-24
I guess they no longer make them.