Alright, now that's a question I'm sure most One Piece fans are wondering.
Most people seem to assume it's because Oda simply didn't plan for haki at that point in the story, so as the story got longer, it became some kind of unfortunate plot hole. Others might say it was a "bet on the new generation" because of what he said to Whitebeard.
Both are good guesses. But both are WRONG.
Shanks obviously lost his arm on purpose. He clearly purposefully didn't use haki and lost his arm as a conscious choice. But why would he do that, you might ask.
Obviously for the DRAMATICS, duh. The man LOVES to make un entrance. Using haki to assert dominance when visiting Whitebeard on his ship? That magnificent entrance in Marineford? Please the bastard loves his entrances.
What better way to make an entrance to save a kid than to purposefully and dramatically scarify one of your own limbs?? Nothing. AND Luffy is now much more impacted by the moment than he would be if Shanks didn't lose an arm trying to save him.
I'm telling y'all. Shanks is a dramatic king and we don't talk about it enough.