It's possible that your flame sensor needs to be cleaned or is on the outs. Some plagiarism from the linked article there..
..signs that your flame sensor is bad include:
- Gas burners light but then go out after 3-4 seconds
- Visible soot is covering the tip of the flame sensor
- The white porcelain on your flame sensor is broken or cracked
Where is my furnace’s flame sensor and how does it work?
Your furnace’s flame sensor is a short, thin metallic rod that’s
either straight or slightly bent and sits inside your gas burner
assembly. Its sole job is to sense whether the gas burners light to
create a fire or not.
If you're feeling adventurous you can try to clean the flame sensor yourself. I recently did this for the first time and my furnace wasn't too challenging. I recommend Googling your furnace's make/model to look for images of the flame sensor, or videos of people servicing your existing model. In my case, I have a "Tempstar" furnace, but its internals are all "Honeywell"
A few IMPORTANT notes, though:
1) Make sure you throw the furnace breaker before servicing it. Some of the wiring might be exposed behind the cowlings and it has the potential to zap you.
2) Your igniter element and flame sensor element (particularly the igniter from what I've read) are sensitive to the oils in your skin, and you can shorten their life inadvertently by touching them. Consider wearing some latex gloves if you have a pair.
3) You'll want to clean the flame sensor element with something relativly soft (i.e. NOT sandpaper). In one video I watched, the person used emory cloth, which is probably perfect. I used a new, everyday, green, kitchen scouring pad. Go slowly and gently.
Honorable mention: Depending on your furnace, you might want to pick up a spare igniter and flame sensor to keep on hand if these are not too cost prohibitive, as it can be hard to find them when you need them on a Friday night or a Saturday.