I have an app service with hybrid connection enabled(on a VM in the same network with the SQL Sever) for me to access on prem SQL Server, which I don't own. However, the connectivity has been pretty unstable.
I am able to access to the SQL Server probably for maybe 5% of the tries and mostly I just get error
One or more errors occurred. (A connection was successfully established with the server, but then an error occurred during the pre-login handshake. (provider: TCP Provider, error: 0 - An existing connection was forcibly closed by the remote host.
I'm able to log in thru SSMS on the VM. Connection string should be alright since I can access locally(local network is the same network as the SQL Server).
Named instances use dynamic ports and UDP, which are not supported by Hybrid Connections. Suggest you using static port as Nick mentioned. Please refer to this document Connect to on-premises SQL Server from a web app in Azure App Service using Hybrid Connections to get more information.
provider: TCP Provider, error: 0 - An existing connection was forcibly closed by the remote host.
What is your Windows version? When Windows versions that don't contain the leading zero fixes for TLS_DHE will display this error message. You can try to update windows version or disable the TLS_DHE ciphers to solve this issue. Please refer to this document.