What do you mean it "fails"? Is there an error message, or do you just mean that the email doesn't arrive? What is the "group address"? Is it an alias or a list of addresses? With what program are you sending the mail under Mime::Lite? Have you tried passing the Debug flag to send() ?

Sending email is fraught with potential errors: your mailer may fail or reject the message; the recipient's MX may reject the message as spam ... there are a lot of ways the process can fail to succeed, independent of Perl.