It depends on the software used and the methods to issue discounts. I know STP has notified me when items in my cart were no longer available, so in theory they could do it for price changes.
But in theory, practice and theory are the same thing. 
Hey, thanks. I’d forgotten entirely about them, and they have wool socks and silk longjohns for cheaper than anywhere I’ve seen, so I ordered some.
Probably not the outcome you were looking for there.