TThe only time that the program will not work is after turning off then turning back on the battery without the programmer.
Turn it off and back on without the programmer, then plug the programmer in. Does it still work?
It sounds like your Axon is stuck in reset mode when the programmer isn't plugged in due to external hardware you are using. Put a 1uF capacitor tied between the RESET and GROUND pins - in theory that should fix it. Also, what brownout fuse voltage is it using (click on the fuses tab in AVR Studio)?
You can solder the ceramic cap underneath your Axon, on the ISP 6 pin connector. They are the two pins furthest from the white triangle, and one should measure as ground with your multimeter.
1 is the reset pin, 4 is the ground pin.