My understanding is an invite will just push a notification to a user saying 'Such and such invites you to ...'. Its different to a friend request as that has its own context where you accept, reject. People get notifications all day, so it's easy to understand why they might brush over an invite for some other content.
A little side note, someone liking your page doesn't mean they are going to see your content. Only 10%-15% of people who like your page will actually see your posts on their news feed. Have a read about it on the net, thats a facebook policy that's been in place for about 4 years now. If you want to extend your 'reach' you will need to boost your posts for a fee.
Sorry reply might come across as bit negative, I just wish to give you some realistic expectations. Keep doing what you're doing, keep promoting, keep growing.