What can I do to make sure that the recurring invoice emails are being delivered?

These recurring invoice emails are sent through Shopify, from the email you set up in your store. So it might happen that the some of these emails went to the spam folder if you don't have SPF records configured for your domain. It is best to check the instructions from Shopify on how to configure the email in your shop: https://help.shopify.com/en/manual/intro-to-shopify/initial-setup/setup-your-email#add-the-shopify-spf-and-dkim-records-to-your-third-party-domain.