I think, you need to add a delay after one write cycle. Because most of the eeprom takes several mS to write data in to the memory.
HI,
I do not know whether you have solved the problem.
If you are not,
check, whether you have correctly initialize/configure the delay function of your processor.
Check whether there are any noice are in the communication lines.
Are you using correct speed of I2C of the external EEPROM.
Check the writing protocol with the EEPROM datasheet.