I am not familiar with PonyProg, are you using the SI-Prog baseboard hardware and the I²CBus eeprom adapter - I note that the adaptor does not have any pullup resistors on SDA and SCL and the baseboard does not provide these either - You have implemented the R2/R3 4K7 pullups shown on your schematic, havent you?? I have had many frustrating experiences with I2C Memory chips instantly solved by a pair of pull up resistors.

Failing this, I dont understand why the memory chip is visually inaccessible, but these results suggest you may not be dealing with a 24C16 chip - other chips may need different addressing.