Have VPN user who receives DBMS error (login timeout) when trying to connect to SDE on SQL Server. User can ping the server and can use sqlcmd with login timeout variable set to 60 (-l 60) to connect to the sql server through VPN (if timeout variable isn't set then it fails).
I am wondering if there is a setting in ArcGIS database connections or if this is handled in the host SQL Server or if there is something else to investigate. Also, permissions are fine since the user can successfully connect while in the office and not on VPN.
How large is the geodatabase? I wonder if it is timing out because of all the data being sent across the VPN and network. Are there lots of feature classes?
What is the authentication method used (DB or OS)?
If the user gets connected do they have any other issues when previewing or editing the data?
Is this the only user with the issue when using VPN?
What happens if the users uses the VPN from a different internet connection?
What version is the SQL Server, ArcGIS client and the geodatabase currently at?
Another option is to collect client intercepts and SQL Server traces at the same time to review what is happening between the ArcGIS Client and the SQL Server geodatabase.
You may need to contact Esri Support and have the help with this issue and review the intercepts and traces.