It is usually delivered, but not where you expect. Send test sends to the store email Shopify has on file, which is not necessarily yours, and the editor prints the exact recipient next to the button as "Test email will be sent to ...". The subject is prefixed with [TEST] and the body is filled with sample data, so search your inbox and your spam folder for that prefix.
Three other reasons. There is a limit of five test emails per hour per shop, and past it the app answers Test email limit reached with the minutes left. If Shopify gives us no usable shop or admin email, the button is disabled and the app says so. And if a send fails you see an error on screen, so no error means the email went out. "Edit a subscription email" covers the editor itself.
Stuck on any of this? Open the chat in the bottom right corner of the app and we will help you set it up.