Check the Azure Monitor and Azure diagnostic logs for the API Management and the API App. This will provide you with more detailed information about the error and help you to identify the root cause.
Check the connectivity between the API Management instance and the API App. Verify that the API Management instance can reach the API App's endpoint, and that there are no firewalls or network settings that are blocking the connection.
Check the configuration of the API in the API Management instance. Verify that the API's endpoint URL is correct and that the appropriate security settings are configured.
Monitor the resource usage of the API Management and the API App. Make sure that the resources are not reaching their maximum capacity, which could cause the connection failure.
Make sure the app service plan is scaling up to handle the requests.
Check the network latency between the client and the API Management instance and between the API Management instance and the API App.
You can also use the Azure Network Watcher to troubleshoot and diagnose network issues