That's to be expected. The COPY command is basically going to send bytes out at the speed of the serial baud rate, which if you're set to 9600 baud is about 1msec/byte.
The pic however takes much longer than that to update the EEPROM (typ 4ms/byte for the K80, no max specified) so the pic uart overruns. Faster baud rates are even worse.

Teraterm has a 'send file' function which you can use, and tweak the time per byte to slow it down enough to work.