Have a gas Beach furnace with fan limit switch issues. First time the blower would not shut off and blew cold air in the end. Replaced fan limit switch and it worked for a month and then did the same thing. Next time it lasted for nearly a year and same thing over. Now with a new one it works and doesn't work. In any of the cases when it wouldn't shut off, I would tap it and the blower would shut off. Furnace guys are bewildered as am I.
It is a Beach furnace, serial 19250, model xgp70.
Temperature inside and out doesn't seem to matter.
Thanks for any suggestions.

Check for air flow restrictions, and get a measurement of the incoming and outgoing air temereature. Check this against the nameplate rating. This should point you in the right direction