Most likely you are having brown out problem. Try enabling brown out reset.
PIC needs some minimum voltage to support 8MHz operation. It seems you have
100uF capacitor on Vdd. During power down situation, it may take some time
for it to discharge fully. This may create a situation where PIC is powered
with a Vdd that is outside the V/f spec. If you violate the V/f spec then
you cannot rely on proper code operation. If instruction read from the Flash
gets corrupted then you may see the problem you are describing. i.e. EEPROM
write function is interpreted as Flash write (just one RAM bit gor
corrupted). The BOR circuit is a tool to protect against violation of V/f
spec.

Enable the on-chip BOR circuit and test it. If it fixes the problem then it
was related to V/f spec violation during power up/ down situation. 

Hope this helps
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