This "offline" error occurs because you are using the IP address directly and not the network name of it (usually EPSONXXXXXX). There is a "DHCP Lease" that expires every so often. This lease tells the network to assign a specific IP address to the printer until the lease expires, then the IP can change, and in your case, it looks like it does frequently.
I would suggest deleting the epson from the computer, trying to download the latest driver, an run the network configuration again. Make sure the Epson Event Manager is installed, so your computer can communicate with the printer. Allow it through your computer's firewall.
Physically on the printer, one of the network menus will show you that the printer has a name of "EPSONXXXXXX". Use this instead of the IP address if possible.