I did some digging around for you on this. While there's not much available in our app store, I did find one app that I think will work: Loyalty by Collect. Take a look and feel free to reply back if you have any further questions!
I know this is an old thread, but it shows at the top of Google when searching for Vend+Shopify loyalty programs so I thought I may be able to lend a hand!
Collect has rebranded as Marsello on the Shopify app store (https://apps.shopify.com/marsello). It works across both Vend and Shopify, and is a lot more powerful than the default Vend loyalty program. You can segment your customers, automatically send emails to at-risk customers, and design a custom loyalty programme (and a bunch more).
Plus, if you use Mailchimp and have heard the news about them discontinuing their Shopify app, Marsello also allows you to sync between Shopify and Mailchimp for free.
My agency is a Vend and Shopify Expert and we've worked with Collect/Marsello for a few years now and I've been really impressed with the team. I see a lot of Vend retailers with this issue and don't want this to be "salesy" at all, I'm genuinely passionate about good apps and can't recommend them enough.
You can keep an eye out for listed apps on Vend here https://www.vendhq.com/us/product-add-ons and at the moment Marsello is the only one for loyalty.
-Angus @ Hello Digital
Hi all, I'm Neomi from Rise.ai app,
we are an app specialized in store credit rewards and gift cards to help you maximize revenue and loyalty at your store.
our loyalty and gift card solutions work on your Shopify website and POS as one.
You can read here more about our solutions
Check out our listing page and feel free to contact me at firstname.lastname@example.org