> Any ideas?

24AA16/24LC16 datasheet, 370kB

http://ww1.microchip.com/downloads/en/DeviceDoc/21703E.pdf

Twc = 5ms, about the same as the EEPROM in a PIC

The 18Fs have quite abit of RAM, from 512 bytes to at least 3840.
If you're able to use one of these, the data could be stored until you
have time to write it to EEPROM. Otherwise you'll need to maybe
look at external RAM

eg NVRAM

http://www.st.com/stonline/products/families/memories/nvram/

or roll your own with a battery and something like a 6116 or 6264
(out of an old HDD for instance) or cache RAM off an old MoBo

Perhaps even Flash RAM. Entry-level device capacities are much
larger than they used to be though. Don't actually know what the
smallest RAM is now

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