You should be reaching out to customers who have only placed one order to find out why they haven't ordered again. Especially when you're working on your repeat customer performance.
Asking an open-ended question is the best way to get a lot of details but you can also suggest some reasons (e.g. haven't eaten/used all of the first order, it was a gift).
Your goal shouldn't be to push these customers to an order (you can help them if they are open to it). Your goal is to learn about their objections so you can try to fix it for future customers.
The hard part will be knowing when to ask. I'd recommend 25%-50% your Average Customer Purchase Latency. That'll make sure the majority of customers have had time to reorder on their own.
Using Repeat Customer Insights you can even do better by using the 1st to 2nd order Average Customer Purchase latency. Look in the Focus on: 1-to-2 Customers dashboard for the timing recommendation for your store.
(Or check out that report in the demo if you want to see it before installing)
Eric Davis
Find patterns in customer behavior
You don't have to be in the dark when it comes to your customers. Using their existing behavior, Repeat Customer Insights shows you patterns and optimization potential for Shopify stores, leading to more and better repeat customers.