Okay, let me get this straight...
You're EXTREMELY new here and you want to get "known" and "respected" by supposedly getting peoples accounts back without their birthdays. Now, the fact that you get the accounts Username and Password to succeed in doing so displeases me. It would be much easier if you just told us your secret.
You're best guess is to wait until Neopets has a BIG update or goes down for a while then AB in the Magic Shop for a while, because people who AB obviously don't check Neopets constantly while they AB, so it'll take them a while to start ABing again.
...In the mean time AB in easier shops.
Theres NO point at all in emailing or sending a Lost Account query asking them to send you your birthday because they'll tell you that that was very old information and information about accounts that aren't logged into regularly is deleted until the account is logged into again.