If there were high frequency harmonics caused by clipping or a "dirty" source signal then the resistor would be more likely to vapourise as it would be recieving lost of power at a lower frequency than with the original cap you had in there.

If you read the datasheet you will see that the footprint of the resistor on the PCB overlay is the same as for the other "signal" resistors so that to me implies that it isnt really taking a lot of power. The fact that you say it is worse with higher capacitor values would tend to rule out instability due to oscillation as the datasheet mentions instability as a likely side effect of too low a value for the capacitor.

You say you are driving the amp with a PIC. Do you have any RC filtering to shape the signal to more of a sine wave, if not you will be feeding it with a square wave which will cause the HF harmonics doing the damage.

What happens if you drive it with an MP3 player ? Does it sound OK and survive being played loud ?