I was lucky that I didn't lose my hair through my first round of chemo either. I'm not sure the second will have the same outcome. I was told by my nurse that it's best not to dye your hair during chemo as it may make it more fragile and more likely to fall out.
The guy who cuts my hair tells me that there are a lot more products available with less harsh chemicals and he thought it would be OK to dye my hair. I opted to wait about 4 weeks after chemo to do it as I'm not sure if I could deal with losing my hair on top of everything else (hate my ears!)
As far as a medical reason, I don't believe there is any reason you can't dye your hair.