I have 30 years old house and before I got to bed I set Temperature for 72F' as soon as it heats up it stops, (that is correct); however, let's say in 3 hours I have another setting for 72 F' as well, the Heating unit won't kick in, the temperature will drop in the house drastically, until I manually go into the basement and reset the switch off and on again, the it will restart. Please help...

Do you know exactly what reset switch you are operating? Does the furnace show and small blinking lights inside the blower compartment door?

It's like a regular Light switch , next to the Unit in my basement

That is not a reset switch, it cuts abd supplies power to the furnace but that in itself could cause the mother board on your panel to reset. Any blinking lights inside the blower box?

We are presuming the furnace is gas fired. Is this correct?
Many gas fired furnaces have a small window in the blower compartment door through which you can see an LED light. If yours has such & the LED is blinking, count the blinks between pauses, then remove the blower compartment door & on the inside is usually a key to the blink code. Tell us how many blinks & what that number of blinks represents.