Need a non-volatile memory IC with near unlimited read/write operations capability
Three non-volatile memory types match your needs, in order of available size:


Wear leveled EEPROM/FLASH.  
Battery backup SRAM.  
FRAM.  


In terms of cost, FRAM is best. All you need is inside the chip, including backup capacitors to complete writing. However available sizes are low.
Battery backup SRAM is large and costly in materials.
Wear leveled EEPROM requires firmware to handle the wear leveling.