I am not experiencing the problem you mention with my configuration but I'd be happy to help you diagnose your issue.
The printer can be network configured three ways: AUTO which is DHCP (the default), PANEL which is a fixed IP address (the way I've done it), or PING which is arp a more obscure type of DHCP. These can be set using the printer LCD or by running Epson's NetConfig utility.
From your short description I would guess you are using the default AUTO which is DHCP. In this scenario, the printer requests and gets an IP address from the router. However, DHCP is not permanent but rather a lease which is usually good for 24 hours. So if the printer is off for more than 24 hours the router will give it the next available IP when it is turned back on. If another printer has been off for over 24 hours, the recently powered on printer can get the other printer's IP or it could get an IP that doesn't match any current printer installation.
If this is the case, then there are a few ways to fix it. If you have set them to be fixed IP addresses then I'll have some questions.