Firstly, the person you are inviting may have once been removed by the group admin, if this is the case, the group admin cannot invite them back, they must go to the group themselves and then request to join.
Why can’t I be added to a private group on Facebook?
To join a closed group you have to be approved by an administrator or invited by a current member. Secret groups offer the same level of privacy as closed groups under a cloak of invisibility. No one can search for secret groups or request to join them. The only way to get in is to know someone who can invite you.
Is there an invite all option on Facebook?
Inviting Almost All Your Friends in Two Clicks
The addition of a “Select All” button for Facebook invites now makes it easy to invite large groups of several dozen or several hundred friends. Just click “Select All” in the top-right corner of a list of friends, and then click “Invite.”