Why does my furnace only work after power reset?
Your furnace controller board is very likely indicating a trouble situation and shutting itself down. This is the equivalent of a car turning on its check engine light and not wanting to move. Shutting the main power off clears the error code and allows it to work temporarily but doesn’t fix what’s actually at fault. 

First, change out your furnace filter. Many error codes are simply because the homeowner never changed the  filter. Check the manual to see if there’s a filter timer reset button. 

If the shutdowns still happen then the next time the furnace shuts down, keep the power on to the furnace so that you can read the error code. Your furnace should have a visible status led that is blinking (otherwise carefully take the cover off your furnace, avoiding any live wires, and look at the controller board). Count how many times the status led is blinking  each cycle (sometimes how quickly it is flashing is also important). Reference your service manual to diagnose the error code. You may have a faulty sensor, sticky motor, bad controller board, too many closed dampers, a blocked air return, incomplete combustion, cracked heat exchanger, blocked condensate line, etc etc. some of these things are life-critical situations. The blickenlights will tell you. 

Ps. Since this is a gas furnace, make sure your carbon monoxide detectors are working and don’t continue to operate it in this unstable and potentially dangerous state. It could be leaking carbon monoxide into your home which leads to permanent nighty-nights.