That is why I asked the OP if he could live without non-volatile storage for the lower 8 bits. Use a static counter for the first byte and use eeprom only when it rolls over. That way there would only be 12K cycles on the eeprom. Well within the 100K spec.EEPROM can not be written to 3 million times. (most parts) There are some ways to get around this. Search on the internet for how. FLASH also has this problem.
At this low counting speed, a 8 digit electromechanical counter would work ok.The time between events is about 1 second, but the contact point of the event is 5millisecond.
The analogy for the events is like this. I need 5 millisecond to change the gear, but the motor will run for a second on that particular gear, and then another 5 millisecond to change to another gear, and the cycles continue. I need to count these contacts and store the number into a nonvolatile memory so I can read this memory in the future.