I need to restart Arduino IDE after each compilations
I finally solved the problem, but it's really specific and I don't know if should be on Stack Exchange. Maybe it could give some clues if someone has a similar problem one day... 

I was using pin 20 and 21 on my Arduino Due which are supposed to have built-in pull-up resistor. That's what I've read everywhere and it has been said again recently in the answer of an another question I've asked : How to chooce SDA/SCL pair on Arduino Due ?.

Solution : Since I'm using SDA1 / SCL1 with Wire1 everything works like a charm. The value I get from the device are correct, no need anymore to restart the board and I can recompile again and again without any problems. 

Edit : In fact, it work significantly better but I still had to use pullup resistors with these inputs. The goal was to use the MPU 9250 and it seems more stable now.