24LC1025 Arduino - Data Writing Problem
Writing a single byte is really bad. You are causing a page write with each bye, and each page has a limited lifetime (100,000 - 1,000,000 cycles) so use block instead.


  When writing any amount of data, including a single byte using this
  function,   the EEPROM will refresh the entire page (128 bytes) of
  data.   EEPROMs have a limited write endurance (often 1 million cycles
  per page).   Therefore, if you write one byte at a time, instead of
  writing a full block   at once, you are wasting the chip's lifetime
  (doing so is also MUCH slower).   ONLY use this if you really only
  need to write ONE byte, and avoid it   when you can.   Using a block
  write (below), you can write 128 bytes and only use a single   page
  write (or at most two, if the write is not aligned to a page
  boundary).


This library should do the trick for you:
https://github.com/exscape/electronics/tree/master/Arduino/Libraries/EEPROM/EEPROM_24XX1025