It can be annoying if your furnace constantly cycles on and off. Not only do you end up with a cold house, but it also puts unnecessary stress on the furnace.
The most likely cause for a furnace that keeps shutting down is an issue with the thermostat. The furnace will shut down if the thermostat registers that the desired house temperature has been achieved. If the thermostat is poorly calibrated or malfunctioning so that the temperature isn't registering properly, you end up with a furnace that constantly shuts off and restarts. Repairing or replacing the thermostat should solve the issue.
In some cases, the home is warming up as desired, but due to heat leaks, it is cooling down so quickly that the furnace is constantly popping on. Begin by checking little-used rooms to make sure a door or window hasn't been left open accidentally. Major gaps around doors or windows can also be the culprit, so check and replace weatherstripping as necessary. Another place that can lead to major drafts is your chimney flue, so make sure it is closed when the fireplace isn't in use.
Your furnace needs to both blow air from the vents and use the vent returns to pull more air in for further heating. If the vents are blocked by furniture or other items, then the house won't be evenly heated, which can lead to frequent cycling on and off. An inability to pull in sufficient air can also lead to this problem, as the furnace will shut down due to lack of sufficient air circulation. Make sure nothing is within one foot of a vent to block air circulation. All vents also need to be fully open.
Clogged Air Filter
Your air filter pulls out contaminants from the air so that dust and other irritating things aren't constantly circling through the home. When the filter becomes clogged, it also can no longer pull air through. Without sufficient incoming air, your furnace will shut down. It will then restart in a few minutes to try and warm the home to the set temperature, but the lack of airflow will quickly result in another shutdown. Changing the filter regularly prevents this.
Mechanical wear and tear, poor lubrication, or poor airflow can all cause the blower inside of the furnace to overheat. When this happens, the furnace shuts down as a safety precaution. You must have the furnace inspected so repairs can be made. An annual tune-up can help prevent an overheating blower motor.
Contact a heating service in your area so you can have your furnace inspected and repaired as necessary.