Sometimes engine shut offs off while driving?

The engine cuts off sometimes while driving. When this happens, I place the gear lever in neutral and start the car and it starts straight away. (My car has automatic gears.) It could again shut off after driving a few miles. There are times it drives without shutting off. I have replaced the main relay twice so far. It drives okay for some time and then it happens again. I have found if I keep the air conditioning on blowing cool air towards my feet it seems to drive longer without it shutting off.
Recently the indicator lights to the air conditioning and related controls on the dashboard do not light up. I am unable to switch on the air conditioning when this happens. These lights just come on at a time of their own choosing and then I am able to switch on the air conditioning to prolong the cut-off period. Sometimes even though the temperature is quite warm inside it does not shut off.
Please help me find a solution to this dangerous driving condition.
Thank you.
Ferdi