Have you trapped wire or something near the hook mechanism stopping it from getting full travel when the button's pressed?
The nice people at HiFiengine have a service manual for the deck, free you just need to join.
HTH
Aiwa AD F660 Manual 3 Head Stereo Cassette Deck HiFi Engine
Could be a dirty power switch, or static electricity. Does it have an infrared remote? Maybe something in the room is triggering it. If so, try blocking the sensor.
Mine did the same, look underneath the tray when open, you'll see a rubber drive belt which has probably perished. You may have to remove the cd carousel, one screw in the middle, for access. Replaced mine with an elastic band and am back in business.