Why does my furnace need frequent power resets?
I had the exact same symptoms with my natural gas furnace, and it turned out to be the flame sensor. 

It's an L-shaped metal bar (but can also be straight, depending on model) that detects if there are flames actually coming out, and turns off the gas if not. It had a white high-temp wire connecting it to the control board. Taking it out, cleaning it with some steel wool fixed the problem for me. 



If yours is like the above, you'll only see the back part of it and the bracket, as the L-shaped end is inside the heating unit.