Write to EEPROM before shutdown I'm currently designing a battery operated device that has to write data to an EEPROM before shutting down, or in regular intervals to save data. Would it damage the EEPROM if it had to shut down while it is being written to? 

The first possible case is when it is transmitting the data over I2C. That shouldn't affect it much. But if it gets powered down while it is actually writing the byte to its memory, I don't know whether it would save it correctly or corrupt it.
According to the datasheet, an EEPROM write takes 3.3mS. If power drops below the level needed to complete the write, the data will be corrupted.