Lisa here from the Shopify guru team.
Happy to give you some suggestions for possible solutions for recurring payments and recurring referrals. I hope I understand what you are wanting!
If you're looking to pay your affiliates upfront, take a look at Refersion Affiliate Tracking. This program will track the sales your affiliates are generating, and calculate their commissions. The commissions can be paid directly to their accounts via PayPal! You could set a unique campaign for a yearly subscription virtual product. When your affiliates share this specific link, they will get their commission when the customer signs up for a yearly subscription. I suspect if the order reprocesses a year later, because it has the same tracking it may repay the affiliate again if you do not set the link to expire. You may want to email firstname.lastname@example.org to double check this is the case or give them a call on 917-463-3395.
For a recurring virtual product subscription, check out Charge Rabbit. This app that integrates into Shopify, is commonly used for stores that sell digital magazine subscriptions, sell digital video subscriptions and charge for ongoing access to files.
Please let me know if this is not what you were after!