Integration between the stock database and the front end website is relatively simple these days.
However many vendors still struggle and unfortunately they drive more customers to the big guys like Amazon.
A lot of it was caused due to the fact that they often didn't in fact have any stock, and were just ordering from the manufacturer's warehouse, marking it up, and re-shipping.
BUT - after a reasonable amount of time, let's say 3 or 4 business days, even manual updates should be the norm.
If they have sales volumes that make that impossible to manage, then their profits need to be re-invested in some automation.
Having said that, my last order form Amazon has been royally screwed up and even after a week, I have no idea when the item will arrive.
Non bike item so not an emergency
And that's on a low cost item that, when I ordered it, was supposedly arriving the next day "if I ordered in the next XX:YY hours and minutes".
My $0.02 FWIW