No, they won't. You can always go to their pre-qual link and keep on trying till you see it.
@Anonymous wrote:So I was browsing the AMEX card line up in incognito mode and received an offer for the PRG.... spend $2k in three months and get 50k MR. I decided to pass on it but now after the fact I am starting to realize that was a fantastic offer. I can't seem to get that offer to pop up again.
My question is - can I call AMEX to see if they will honor the same offer? Or do I just keep trying the incognito method and hope it pops up again?
Amex isn't known for matching offers after the fact, so you'll need to keep trying. 
I hadn't seen any offer for 50k MR points in literally months, but when I applied for my Delta Gold I went 'incognito' and checked for a PRG offer just for the heck of it (it truly was 'for fun', since I was fairly certain it wouldn't be there). Lo-and-behold, the 50k/$2k offer came up so I had to jump on it.
In my case, I was using a VPN routed through Dallas, although many others have reported finding the offer on a 'normal' internet connection. Some people are able to get the offer at work but not at home (or vice-versa) so that's a thought as well. Also, for a while I was able to get the offer on my Amazon Fire tablet, but not my PC or smartphone (the Fire tablet's Silk browser has back-end work done by Amazon servers, which apparently made a difference).
Keep trying... you'll find it again! 
@Ammer wrote:I get that offer every time I log into my Amex account. I'm waiting for a 100000 Platinum offer :-)
Who isn't 