If you purchased the theme from AppThemes then we should be able to trace the transaction and the account if you can provide further details of it for us to search for. Sometimes people make the purchase under one email address for example, and then they log in with another account using another email address and it doesn't show purchases linked to it. The only way in which you'll be able to download the latest update for the theme is to log in with the account used for the purchase.
Please
send us an email to us with your full name, email address used for the purchase, and if you do have a transaction id from PayPal or Google Wallet this would also help. Thanks.