Invites can only be sent by users who have achieved trust level 2. There is no setting to configure this. Users who have not achieved trust level 2 should not be seeing the invite link, so this is not likely the cause of the issue.
The max invites per day site setting controls how many invites non-staff users can send in a day. If a user has exceeded this limit, they should be shown a notice telling them that they need to wait before they can send more invites. They should not get the error message that your user is getting.
What version of Discourse is your site on? Are you able to try loading your site in safe mode to see if that fixes the issue?