The heatpump works but the blower has problems. When the fan is put to "On", or when the system is initiated by the thermostat, the blower sometimes will try to start, but cycles on/off. I can hear the relay clicking. When the system does operate correctly the problem will eventually re-occur. Another symptom is that the blower will not run for the minute or two after the heater shuts off, it stops immediately. I replaced the relay, without positive results. Anyone have any suggestions?

Not sure about heat pumps, but most systems the blower relay is controlled by a limit switch. If the limit switch interrupts the power to the coil, the relay will open. If there is a limit switch, it will be at the heating coil somewhere.