The five causes, in the order they actually occur.
This accounts for almost every case. Online Store → Themes → Customise → App embeds → Badgely badges must be switched on, and the theme must be saved afterwards.
Check the badge shows Active on the Badges screen. Then check the counters: Products with a badge tells you how many products currently qualify. If it is zero, the condition is not being met — a Low stock badge with a limit of 5 shows nothing when everything is well stocked.
Product pages, collection pages, search results and the home page are separate switches inside each badge. A badge can be perfectly configured and still hidden on the one page you are looking at.
Badgely updates when Shopify notifies it of a product change, usually within seconds. Press Resync products to force it.
If the badge has a start date in the future, or an end date that has passed, it will not show. Empty both fields to run without a limit.
If anything here was wrong, unclear or out of date, tell us — the article gets fixed the same day.