You may have encountered the maximum outbound connections allotted to your app service. You can leverage the Diagnostic and solve problems blade to investigate and dig a little deeper to avoid such issues. Ensure that all outbound connections are leveraging some sort of pooling. There may have been a spike that caused TCP connection issues. You can observe the connection limits, which are based on SKU size, here.
Another option you can consider is utilizing a hybrid connection between your app service and MSSQL. The links provided are guides that hopefully will allow you to zero in on the root cause. If the suggestions provided doesn't please comment below.
Regards,
Ryan