Most likely you have a dirty flame sensor, out-of-alignment flame sensor, faulty grounding of the furnace frame or a bad control circuit.
The flame sensor is a rod that has a voltage applied for the purpose of creating a current flow through the actual flame. A gas flame will conduct electricity. The control board monitors the current flow and if the current is not adequate, because there is no flame, then the furnace is shut down.
The causes for an inadequate current flow can be a dirty sensor rod (clean with steel wool or emery cloth), improper positioning relative to the the flame and the burner (the current has to flow from the rod, thru the flame to the burner or other grounded metal surface of the furnace), or a poorly grounded furnace frame (check all 120 volt wiring back to the main circuit breaker box for good connections).