Interesting, have used regular saves and restores to eeprom for several years on the same chips without a problem, but only in a domestic environment; expect other areas could well cause such problems, though not a device I have ever looked at, not sure how or why Fram would be any less susceptible ?
Also a bit surprised that only eeprom would be affected and nothing else on the pic. though as you say if using Fram cures the problem, other areas clearly are not being affected ..