This is down to 2 possible faults..... either tapes are too tight, which makes the player think it has reached the end of the tape and is trying to play the other side..... however.... same scenario.... and it will just keep switching sides....
or the sensor (which is supposed to detect the end of the tape by sensing the increased tension) has become worn and you'd be as well to bin it.... too costly and fidly to repair
Firefox, December 2004