Arduino Nano uploading gives error: avrdude: stk500_recv(): programmer is not responding
Know this is old but I ran onto it during my search for Nano(V3)'s not uploading so thought might help someone else.  Problem is the bootloader - Arduino IDE BUT I Found an easy solution (right under my nose). 

I realized that my nano's had been uploading just fine then I had finally updated the Arduino AVR Boards from 1.6.20 to 1.6.21.  I didn't think there was any problems because it still showed my Nano and ATmega328 etc in the board manager after the change. 

But the new boards manager has a new ATmega328 processor choice for the Nano. I changed processor: In the Arduino IDE select TOOLS > PROCESSOR > pulldown menu from ATmega328P to  "ATmega328P (Old Bootloader)".

Since then, I have uploaded many programs to several different Nano's V3 (Prolofic interace Chipset) without issue.