As of Sunday morning (October 8), the 2017 Limited Edition Silver Proof Set appears to have reached the sellout point. The sets were released at noon on October 5 with a household order limit of two. Over the next 22 hours, the Mint sold 29,164 of a maximum 50,000 units, according to Paul Gilkes of Coin World.
The order limit was lifted at noon on October 6, and sales picked up accordingly. The “unavailable” notice on the Mint’s product page began to appear sporadically by Friday evening. Late Sunday morning, the “unavailable” notice went on and stayed on. Although this is often considered the unofficial sold-out point, it’s entirely possible that more sets will be made available in the next couple of weeks as returns are processed. People who’d like to get a set should click the “Remind Me” icon on the product page and enter an email address when prompted. (Note that email alerts can be slow to reach their recipients, though. It’s best to check the page in person several times a day.)
In online forums, collectors seemed to approve of the Mint’s release strategy: limit the orders initially so that individuals who want the item have a fair chance to buy it directly from the Mint; then, after a reasonable amount of time has passed, raise or remove the limit, opening the door to dealers and others who want to buy larger quantities for resale. This is in direct contrast to what many consider the debacle of the 2017 Congratulations Set. Like the 2017 LESPS, the Congratulations Set contained a low-mintage 2017-S Proof American Eagle silver coin. Unlike the LESPS, the Mint released the item with no order limit, and it sold out in minutes—with large numbers of the coins bypassing individuals and going straight to dealers for markup.
While plenty of the 2017 Limited Edition Silver Proof Sets were bought for sale on the secondary market, a great many of those first 30,000 purchases were for personal collections and gifts. As observed in a number of comment threads, perhaps the Mint could make this the model for future releases.
Edited 10/18/17 at 10:40 p.m. to correct the date in the first sentence, which was misstated as October 9. That Sunday was October 8.