Are EEPROM chips getting obsolete?
It's more expensive and not available in really large sizes.

Compare e.g. http://www.digikey.co.uk/product-detail/en/cypress-semiconductor-corp/FM25V10-G/428-3323-ND/3788992 vs http://www.digikey.co.uk/product-detail/en/stmicroelectronics/M95M01-DFDW6TP/497-15781-2-ND/4357400 - the FRAM part is faster but almost 10 times as expensive.

It's found a nice niche as a replacement for battery-backed SRAM and in heavily used dataloggers, but it's not ready to obsolete EEPROM.