I had this problem on my furnace and it ended up being the "flame detector". It's a small ceramic housing with a wire sticking out of it that detects that a flame is present when your furnace turns on. It can be "coated" and can't detect the flame therefore it will shut the furnace off to prevent a potential gas leak. I had a furnace repair guy come and do mine, and then I watched him and now do it myself. Saved myself about $100 per repair. It's simple to do one you see how. I just take a wire brush and rub the wire until it's shiny and put it back in. Hope this helps.