You can manually set the IP Address (also known as a 'static' IP Address) on the printer so when your router resets, your printer's IP Address will remain the same. When your router resets, it will assign your printer a new IP Address so you will need to turn the printer off and back on to reset the IP Address on the printer too (so it accure a new IP Address from your router).
If your situation is the same as DorothyMcGee described, it sounds like your router automatically assigns the IP Address for your printer.
