It appears as if the second wave of the closed Home Beta invites have been sent out. Numerous reports from people who weren't accepted into the original beta indicate that the download is now available to them on PlayStation Store.
For everyone who got the first Home e-mail but failed to receive an initial invite, check the PlayStation Store now! If you're one of the lucky ones you might have a little present awaiting your arrival.
No word yet on when the next wave of people will be accepted, but we assume that Home will grow gradually over time. An open beta is due to launch in July or August, although how "open" it will be has yet to be determined.
As always, your source for all things Home.