Proposed solution:
I had the same problem and was able to analyze and fix it the following way:
1) Open the page where you have embedded the map.
2) Open the Java-Script-Console in your browser (how to: https://developers.google.com/web/tools/chrome-devtools/console/javascript)
In the tab “console” Google provides you with a very clear error-message which problem it detected. That can be e.g. “referal not allowed” or “payment data missing” or others. Very nice: The Google-Error Message provides you with a clear url-link to a help page how to fix your specific problem. 🙂
-> In my case, everything was configured ok, just no payment data provided.(Which you would likely not assume necessary if quota are not reached. But Google requires it anyway…