Leave the printer with it's DHCP Reservation. If you trust your network infrastructure, a DHCP reservation is every bit as good as a static and easier to manage in the long run. If DHCP isn't working then fix the DHCP server rather than assigning statics.
I rather suspect the printer's connection to the network is fine. But you can test this by taking another machine on the network, opening a Command Shell (<Win> + <R> ==> cmd ==> Enter), and typing ping /t printerName. This will continually send a packet (once per second) to the printer and check for a response. Leave that running and next time there's a 'connection issue' check it. You could also set-up a ping to the 'server' using another Command Shell.
Don't bother with an FTP server - that's just adding extra complication when it's better to keep things simple.
The best suggestion I've seen so far, is checking that that "server" hasn't gone to sleep. There are two other distinct possible causes of this problem I can think of.
1) A none-server version of Windows will only support at most 10 remote connections to network shares etc. If you have over 10 workstations (or even getting close to 10 workstations), not all of the workstations (inc. printer) using the server will be able to access it simultaneously. Solution: stop being a Cheapskate and invest in a proper server.
2) I suspect the devices on your network are relying on a mixture of DNS courtesy of the Virgin Media 'hub' and Netbios courtesy of Windows to find each other. In a Windows 'workgroup' network (N.B. where there's no domain set-up) one of the machines on that network will be elected "master browser" and other machines on the network will query the elected "master browser" when looking for network resources like file shares and printers. The master browser can change as workstations are switched on/off and problems arise when a newly elected master browser does not know about all the devices on the network. I've had this problem a few times and I've hacked machines around so only the machine that's always switched on can be master browser. Solution: It's hacky. Stob being a Cheapskate and invest in a proper server.
A HP Gen8 Microserver and Windows Server 2012 Business Essentials or something like that should do the job.