If a REST-API in WordPress is not working and an error message is displayed, there may be a number of reasons for this. Here are some possible reasons and steps for troubleshooting:

Possible reasons

1. Plugin conflicts: Plugins can block or affect the REST-API. Temporarily disable all plugins to see if one of them is causing the problem‍
2. Server configuration: Issues with server configuration, such as cURL errors or incorrect redirects, can also affect API functionality‍
3. Authentication issues: Make sure that the API requests are correctly authenticated. Missing or incorrect authentication data can cause errors‍
4. Rate limits: Check whether the API requests exceed the set rate limits. This can lead to a temporary blocking of requests‍
5. CORS issues: Cross-Origin Resource Sharing (CORS) can block requests if they come from an unauthorized domain‍
6. Broken permalinks: In WordPress, broken permalink settings can, in addition, cause the REST-API to be unavailable. This can be resolved by resaving the permalink settings

Troubleshooting steps

1. Check plugins: Deactivate all plugins and check whether the problem persists. Reactivate the plugins one by one to identify the problematic plugin
2. Check server logs: Check the server logs for specific error messages or indications of connection problems
3. Resave permalinks: Go to Settings => Permalinks in the Wordpress backend. Re-save the latest settings to regenerate the .htaccess rules
4. Customize CORS settings: Make sure the server allows CORS requests from the domain of your WordPress site
5. Test API-requests: Use tools like Postman to manually test API requests and diagnose errors

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By following these steps, you can identify and fix common problems with the REST-API in WordPress.