If your shifter has a 1-2 (2-speed) lever, for sure you have a gear-type transmission, NOT a hydrostatic. If you've eliminated all the external issues, and still having trouble with it holding second, it may just be the trans. is worn excessively, and might need replacement. Process of elimination...you might get lucky and find a used one or old matching mower with a shot engine but good transmission. Worst case would be to replace with new, it does come with a warranty. Not cheap, but cheaper than a new mower.