@James - your answer does not work, nor do any of the other obvious answers to the question "how do I get shopify to resend the account activation email"
Once the customer object has been created shopify completely ignores send_email_invite=true in customer put's so there is no way for us to have your servers re-send the account activation email (for example, if the customer forgets to click on it originally and can't find it months later, at which point their account is locked, they can't "change the password", "re-register" and/or interact with it in any way).
We can't clone and send this email ourselves, because the {% customer.account_activation_url %} isn't actually a property of the customer object outside the scope of the account activation email, so we don't know what the right url would be.
We also can't delete and recreate the customer, not just because it's a horrible hack, and not just because it entails keeping all the fields intact including all metafield and purchase records, but because it also causes a change in the customer's shopify ID which impacts all our customer tracking and non-shopify database records for the customer as well.
This is a pretty huge problem that there is no way to re-send that invite email given that you completely lock users out of their own accounts if they neglect to respond to the email intitially. The only solution we can find is to page a human operator, have them look up the customer manually in the admin pages, manually click the "send account invite" button at the top of the customer page, and then manually click the appropriate buttons in the popup page that appears when they click on the "send account invite" button.