Since your display is maximum 9999 hours (599,999 minutes) you will overflow the display long before the first EEPROM location "wears out".

You can move to a new EEPROM location each time the display rolls over from 9999 to 0000. When you're done with a location, write FFFF to it, and tell your software that this is the flag indicating to use the next one (and so on). Your Hour Meter should be able to run for at least 50 to 75 years. (At least as far as the EEPROM is concerned.)