If your furnace ever turns the flame on and then shuts it off a few seconds later, it's probably the flame sensor. Many furnaces will blink an error code which means no flame was detected by the flame sensor.
You can often clean the flame sensor with steel wool or fine sandpaper to fix it.
This happened to us about 7 years ago, and I was clueless, so this post is helpful. My coworker texted me (we were worried, single digits, and house now 52F, electric portable heaters were like a pebble thrown into a lake. He said please remove your filter, then see if your furnace will stay on. It did. The final fix was a combination of increasing the blower speed by moving jumpers, and using cheap filters. We got by another 5 years that way. Ultimately low end hvac was installed 1999 and AC failed 2019 (Bryant with a SEER of 10).
I went around in circles, if I have used these $8 filters for 14 years, why, all of a sudden, can't I? It was counter intuitive--I put in a new $8 filter, and 1 week later, furnace won't stay on.
A indie hvac guy came, looked, and said buy the cheapest filter you can find, I'm talking 50 cents to $1.50. Now he explained to me nothing on the internet seemed to, when they said the same thing. The reason you go cheap filter isn't because good filters strain your blower motor. It's because your blower motor can't do what it was designed to do, as it's old. He said it's like an old man, it can't blow like it could when it was a young man.
.
We got new hvac in 2020, and the new 94% system has one of them ECM motors and the filter is now 3" thick and costs over $30 each. I didn't choose that I guess I didn't even research at the time.
So if ever in a pinch and the furnace is short cycling, please try removing the filter altogether to see if you can get by until a repair is done. OR, go to the big box store and pick up the really cheap filters, they come in 3 or 4 and are likely barely $1 each. You can change them out every week if needed to keep going.
What I also learned is replacing the blower really isn't a DIY job, and normally if it's over 10 y.o., may need a new furnace, as it could approach $1,000. Also, furnaces last much longer than an AC condenser, but AC relies upon the furnace's blower and the evap is also integral to the furnace. So when AC fails, again, conventional wisdom might throw out the furnace. Not only that, if like us, we went from a 78% furnace to a 94% one.
Hope all stay warm!!
.
. I bought some of the other parts there and that went well.