Nobody is receiving the announcement

Check in this order:

1. Subscribers → Email subscribers when your site goes live is on. It goes out when your page comes down: by the scheduled switch-off time, by Disable on the Dashboard, by saving Shop closed for orders under Page → Mode while the page is up, or by saving a Switch off at time that has already passed under Settings while the page is up, answering yes when Disable or Save asks. With it off, Disable asks before launching without it and says how many were not emailed, and so do those Saves; Send to … not yet emailed on the Subscribers screen tells them afterwards. A Switch off at time saved more than a week after it passed emails nobody, whatever the answer: the message after the save says so, and the Subscribers screen can send it if you still want to. So does the scheduled switch-off when WordPress runs it more than a week late (a site nobody visits runs no scheduled tasks): the Dashboard then says how many were not emailed, with Send the launch email, which asks first.
2. The page came down without the question. A press of Disable, a Save of Shop closed for orders or a Settings save of a switch-off time already gone by that was never asked (somebody signed up after you opened the screen, your store was set live in WooCommerce since, or you opened the Settings screen after the time had passed), or an imported settings file that took the page down, emails nobody and says how many were not emailed. So does an OK to switching off or saving without emailing when the launch email was switched on in another tab after you opened the screen, even while WooCommerce hides your store: the answer is to the question you were asked. And a yes to a Save whose question named fewer or more people than are waiting when you save (somebody signed up meanwhile): the save goes through and emails nobody, and the message says why. With the launch email on while WooCommerce hides your store, Disable, a Page screen Save or an import that was never asked holds the email for your store instead (see 3). A Settings save asks while the store is hidden too, and holds it only on a yes. An imported file that keeps coming soon or maintenance mode on with a Switch on at time still to come takes the page down only until then, and is not a launch. With the shop closed for orders, the Dashboard's Recommended list shows Send the launch email until everybody has been emailed; it opens the Subscribers screen.
3. WooCommerce's own Site visibility is still Coming soon, or was when the page came down. The launch email waits until the store is live, because the people on the list would otherwise arrive at a shop they cannot get into. The Dashboard says so, and Set Site visibility to Live there asks and then sends it, with your page off or with the shop closed for orders. Set live in WooCommerce's own settings instead, it is not sent, because nobody was asked: the Dashboard shows how many are waiting, with Send the launch email.
4. A red note on the Subscribers screen means your site could not send. It says what the mail system reported, and nobody is marked as emailed who was not. Fix the delivery, then press Send to … not yet emailed to carry on.
5. You put the page back up, or switched the launch email off, while it was going out. Sending stops then, before the next email, and the rest stay as not yet emailed: send to them when you next switch the page off, or with Send to … not yet emailed on the Subscribers screen. The message after your press or save said how many were not emailed.
6. Send test email — if that does not arrive, the problem is your site's mail rather than this plugin, and an SMTP plugin is the usual fix.
7. Messages go out in batches of twenty-five, a minute apart, driven by WordPress cron. A site with no traffic runs no cron; open a page or two. If sending stopped part way with no red note, your host may have stopped a batch that took too long: nothing more is booked after that. Press Send to … not yet emailed on the Subscribers screen to carry on. The Dashboard says so itself only with the shop closed for orders, or for a launch email it offers after a late switch-off or held for your store, and only ten minutes after the last batch was heard from.