I’m happy to be corrected by know-alls and so on but this is my reasoning…
Its all to do with Shoemakers!
If you know that a last is the form a shoe is made on then the phrase takes on a different shade of meaning. A last is often a wooden form made to the shape of a client’s foot though it is also the foot shaped anvil on which the shoes are made.
Something that is made to last is therefore becomes made to a pattern, so it isn’t durability but reliability that becomes the watchword.
I found this link which is about shoemakers and cobblers motherbedford.com/Shoemaker.htm though it does nothing to back up my possibly fanciful suggestion. I’m sure the folks at QI (@qikipedia) and the estimable Stephen Fry (@StephenFry) would have an opinion on such deep matters of etymology.
What do you think, was I possibly a little overtired?