I Have Better IDEA! Just buy new device (This device has an memory ATMLH436, which is basically same as AT24C02 eeprom chip), disconnect the WP pin and connect it only with the VCC pin, it then can't write the counter down (since it will be write protected), every time you pull the batteries out and in again, it will be as fresh as new. Should work like a charm :D
Here is the historical answer, maybe usefull to someone in the future:
How to hack instruction.
This device has an memory ATMLH436, which is basically same as AT24C02 eeprom chip, which is an EPROM with I2C interface, it is 2 KBytes memory. And the counter is most likely stored on this element.
You need to buy a new device, connect the not used eeprom to a i2c programator (you need to buy one, or ask a friend, I remeber this as a simple device connected to a rs232 port, but you can find one for usb), read the memory content and store it in a file and then you can use this file to reprogram the eprom to the original "new" state every time you want.
How to connect the i2c eeprom to mac:
hmmm, you need to have an i2c programator, that's first step.
Check the one you're about to buy if it has a Macintosh compatible software for reading/ writing.
If not, maybe use other computer.
remeber that in order to be able to program the device you need to connect the pin 7 (Write protect pin) to the ground. Here's the chip spec: http://www.atmel.com/Images/doc0180.pdf
Basically in oreder to communicate with the device you need:
know the address of the device - it is set by the A0,A1,and A2 pins connected either to ground or VCC - the programator soft will require that address.
connect the SDA, SCL and GND pins to the programator.
the chip need power supply of 5V connected beetween GND (-) and VCC (+) to operate.
In order to program the WP pin needs to be connected to GND.
There are big chances that: A0,A1,A2 and WP are grounded, but I can't be sure.
In case of this scenario the address of the device is 1010000 and there's nothing left that needs to be done in oreder to program it. I assume if the WP pin is not grounded you can disconnect it from whatever it is connected to and hardwire it to ground - should not affect normal operation of the device. probably you don't need to unsolder the chip in order to be able to read/write it, you need to connect GND, SDA, SCL and VCC. I would make a connector for these 4 pins to have it accessible from ouside of the device.
In order to make my life easier for many reprogram cycles, I would solder some connector to not have to disssassemble the device each time I need to reprogram it.
There are small chances that the counter is in the fat black round dot on the PCB, in which case there's nothing you can do to reset it since it is some custom chip without spec - if you have a great lab with X-RAY machine (like https://www.hawkerrichardson.com.au/electronic-production-systems/inspection-test-a-repair/unicomp-ax-8200) and other such stuff + lot of experience you could :) but rather not many people have such toys since they are very expensive :)
There are some pins to connect to the rounded chip, but I don't have any idea how to use them, what's the protocol or anything...
but if they could produce eprom inside of it, they wouldn't probably use any additional external eeprom because of the costs. But since eeprom production is not so easy as the regular chip, they use rather external memory from other supplier rather that producing one by themself - it's one logical argument that the counter is there in the AT24C02.