Local SSMS connected to VPN SQL Instance - update fails when VPN disconnects
As far as I know, if the connection between the computer issuing the query batch and the server executing the batch is broken, the server will terminate the batch.

As the comments have noted, your best solutions are executing the command from a computer that won't be likely to lose its connection; executing the commands from the server itself is, unsurprisingly, about as safe as you can get.

As sp_BlitzErik recommended, executing your batch from a SQL Server job is good, when the query can safely be run as a fully unattended process works, and shouldn't consume too much of the server's resources.

If a process needs to be monitored above and beyond simple success/failure on completion, then the most common solution is probably a remote desktop connection. Depending on our organization's security restrictions, you could hopefully be allowed to remote into another computer on the same LAN as the server (if not the server itself, if it wouldn't constitute too much of a resource drain).

If your VPN connection breaks, the session on the remote server keeps running - you just lose your visibility into it. When you re-establish your VPN connection, you can reconnect to the remote server, and see what progress has happened while you were disconnected.

As noted, you want to be sure that your remote connection is not consuming resources needed by your server, and that all necessary security concerns are dealt with. You do not necessarily need to be on the server itself; as I said, any computer on the same network as the server will do, as long as it has the software you need to issue your query.

Over the course of the past few years, I have worked on a few projects that required long weekends hours every other weekend, or two out of three even, for months. Remote desktop connections from home made life much easier (and was much more appropriate than basically living in my cubicle :-) ).