The communication is going wrong. Reading the lfuse, hfuse, efuse return all three only zero. That is probably a MISO or MOSI signal going bad.
It could be a very thin copper trace that shortcuts something. Or there is something that has a larger capacitance. Of a voltage level from a voltage regulator is slightly different. Or the ATmega32U4 is damaged. Or not enough decoupling capacitors. Or a bad ground wiring.
My best advice is to change as much as possible. An other programmer, other computer, other cables, and so on.
[ADDED] Maybe I'm wrong, and it is as Isaac96 writes in Reply #4. The newer versions of avrdude read the chip settings from the avrdude.conf file.