Huh? Which digital game stores do that? Steam? GamersGate? Humble Store? GreenManGaming? Origin? I don't think they do. If GOG.com did something like that, it would be quite special and uncommon.

How about the cases where a game is offered as a freebie (has happened several times in GOG's history)? Should they then reimburse the whole price to all those who bought the games earlier (e.g. in one month)?

I agree that buying something that goes on sale (or is given for free) later can be frustrating, but I don't think giving back the money difference to those that bought the game n days ago would be a perfect solution because there would still be that line to cross between getting the game at a full price and at a discount. e.g.

Game goes on sale 1st December.
Person bought it for full price on 29th November: "Damn! If I waited 2 days I'd have gotten it at half price."

So the store offers money back to all those who bought it within the last month.
Person bought it for full price on 29th November: "Hooray I got reimbursed with the difference and paid"
Person bought it for full price on 30th October: "Damn! If I waited 2 days I'd have gotten it at half price."

So there will always be the frustration when something becomes cheaper if only you bought it a bit later.

A solution would be for gradual money reimbursement, depending on how long ago you bought it, but that's probably just too complicated. I wonder though if any store implements it this way...

EDIT:
Something like:
d= price difference
n= number of days between buying game and it going on sale
m = money reimbursed

m = d * max(((30-n)/30),0)