If you have any third-party service running on your Windows machine (that tries to connect to your printer, possibly?), turn it off.
ARP requests are indeed sent out in order to receive IP addresses within the same network. This service could be checking frequently if the printer is actually up or not.
If not, access Device Manager by [WinKey]+R
and typing in devmgmt.msc
. Now look up the device "YourPrinter" and check if there are any options available to turn off Auto-Discovery or such.