Karlie here from the Shopify Guru Team! I'm happy to look into this for you. How are you issuing invoices? To create an order and invoice your customers you would need to be creating draft orders from within your Shopify Admin. Can you check this guide to confirm that creating draft orders is the method that you've been using? If you aren't using the draft orders method then can you explain to me how you've been issuing invoices as well as any further details regarding why your customers might not be receiving the invoices?
Looking forward to hearing back from you!