How old is the unit?
If you had the model and serial # it wouldmake it easier for us.
If it is an older unit it msy be controlled by a fan limit switch. This will only turn the blower on when th plenum reaches a certain temperature. It may be that your gas valve is clogged and is shortchanging the heat exchanger. This would make the blower turn on ad off. It might also be a defective fan limit.
If it is a newer unit then you may hae a bad control board. It is timed, nothing like a fan limit.Let us know so that we can help you more
best of luck