This is a tricky approach. Some store owners may not want to have something automatic in place. Others will. The fact is, so many shops rely on customer reviews and also, customers depend on them. And sometimes getting them is not so easy.
An Email Reminder for a Review
The Payment Reminder extension for WooCommerce includes an option to do just that. It’s a simple extension that gives you the ability to do this without the purchase of a much more extensive plugin or even a SaaS service.
As you can see here, you can set the reminder intervals and limits. Plus, you can toggle the other options off or on.
You can also preset your email fields and customize the email a bit with a header logo and custom email footer.
Here you can create the custom subject line and email content that will be sent out. This is the default message that has been added using placeholders.
The other suggestion I would make is to add a note of thanks if they have already left a review.