Ive never herd of a flywheel demagnetizing - most my tractors are 20 plus years old still running original flywheels.
I did have a curious issue that sounds similar to yours on my 90 murray - cranks but will not start- cleaned the carb, nothing.
Pulled the flywheel shroud and i noticed the magneto actually slid forward and was rubbing the flywheel - so pulled it off, cleaned the mag ends with sandpaper, cleaned the flywheel edge up, remounted and air gapped the mag and STILL nothing- not even a cough. Changed the plug for a new one, put my fingers on the coil end and still got what seemed to be a decent shock- nothing. Unhooked the mag kill wire- still nothing, cranks with no hint of starting.
At this point i was frustrated, to say the least - with the voltage i figured it was enough, so as a last resort i went and dug thru my parts bin and found another good used magneto.
I put it on, set it, cranked the motor and it coughed to life. Even tho the old mag shocked me- must be wasnt enough to ignite the fuel .
Try replacing the magneto and see if that cures the issue . Make sure it doesnt have points either ( if its that old) - wire would run under the flywheel from the magneto.