For most stores it would be the day the sale starts...especially if you have coupons that will be expiring soon for those items. Remember you can get rain checks if they're out (unless it states in the ad "while supplies last"). And ask when they get their deliveries so you're not checking everyday when they only get deliveries once or twice a week.
I never go to Walgreens just to get the FREE items
the week they're advertised unless I need to get other things that are on sale for the week. The free items seem to be advertised the first full week after the rebates start (sometimes the Easy Saver book starts in the middle of the week which is probably the BEST time to get the free items). Their rebates go all for about a months time but it doesn't state in the ad that they'll be free for the next 4 weeks. People probably assume that they have to get it that week so they run out. I've always been able to get the FAR (free after rebate) items before the deadline...which I wish was the last day of the month. It would be a lot easier to remember when they ended and the new one started but that would be too convenient.
RiteAid has some items that are only free for a certain week so you would want to get it a.s.a.p. If they run out ask when they should get some more. If they're out of a rebate item that has to be
purchased during certain dates the Provo RiteAid will let you prepay for the item so you have the receipt to use for the rebate and then they'll call you when they get it. The north Orem (off 16th North and State) will just write "free" on the rain check so you can still get it for free...
I don't know if this is still the case because I don't live that close to a RiteAid anymore and haven't been there in a while.