Thanks for asking question. If I have understood right, you are having issue while making new outbound connections. If so, you may want to know that the major cause for intermittent connection issues is hitting a limit while making new outbound connections.
The limits you can hit include:
• TCP Connections: There is a limit on the number of outbound connections that can be made. The limit on outbound connections is associated with the size of the worker used.
• SNAT ports: Outbound connections in Azure describes SNAT port restrictions and how they affect outbound connections.
You may refer to below document link on troubleshooting.
Also you can access App Service diagnostics feature. Navigate to your App Service web app container, In the left navigation, click on Diagnose and solve problems.
App Service diagnostics is an intelligent and interactive experience to help you troubleshoot your app with no configuration required.
Let us know.