Networked Brother Printer needs restarted in order to print

Hey there! Another printer topic!

Hopefully some background info is helpful: Our ERP runs on our Windows 2012 R2 Server and requires that our printers are installed on that server in order to print to them through the software, using their printer name. One of our remote branches, connected via a point to point VPN (Cisco ASA firewall), has a particular printer that just recently started giving us problems, even though it's been happily working for 4 months.

The printer is a brother MFC-9130CW and has a static IP through on the branch's wireless network. They are able to print to it fine when they have it added directly by the IP address but print jobs sent through the Server (and from the ERP on the Server) have been getting caught, with the printer showing as "Offline." The only way that they can get the Server print jobs to print is...