Is there any way to disable auto-shutdown from login screen when no user is logged in?
I have not found a way to disable filevault auto-shutdown, but I have found a way to restart while bypassing the filevault pre-boot login screen (where the auto-shutdown happens). Entering this command in terminal will allow a remote restart without the risk of a shutdown:

sudo fdesetup authrestart

After entering the command and a password for sudo, you will need to enter either the filevault recovery key or a user password for a filevault-enabled user. This password will then be stored in memory and used automatically upon boot to satisfy the filevault authentication requirement. After the disk is decrypted, you will then be taken to the standard post-filevault login screen which doesn't trigger shutdown after 5 minutes.

Additionally, the authrestart command could be set to load a plist file automatically each time the computer is booted to authenticate filevault automatically, but this partially negates the purpose of filevault, and I don't think it's a great idea to store a password in a plist file.

I found this information here.

I'd still like to find a way to disable auto-shutdown permanently, but at least this is a workaround for the remote restart issues.