Air Conditioning - Inside blower won't stop

I'd appreciate any help someone can provide. The inside blower on my AC won't stop running. The AC is cooling to temperature, but when the outside unit stops running, the inside fan keeps running. When I turn the unit off from the thermostat control, and turn it back it on, once the temperature inside rises to the point that the AC should kick back on, it won't. I hear it humming on the outside unit, but have to turn it completely off again and back on to get it started again. From that point, it once again cools to the desired temperature -- the outside unit shuts off, but the inside blower keeps blowing. What's the issue? Our AC guy has been out twice but can't find a problem.

Sounds like a possible bad blower relay. On newer units the relay is on a circuit board, in which case the board must be replaced. A technician would look for power (or lack of power) at the blower motor and for the 24 volt signal from the thermostat to the relay or circuit board. It's also possible the thermostat could be bad. These tests should help narrow it down.