Yeah I don't understand what it is I'm not doing, looking at vids some folk are maxing out his posture bar in under a minute and I just can't do that even when I'm in his face constantly attacking?!
What I do is try and use tools that help me a be a bit more aggressive and defensive at the same time. So try to get close and deflect a few attacks, and when there's an opening, use firecrackers to stun him and then use a double-ichimonji to do some damage and regain your own posture so you can keep being aggressive. When I kept this up, Genichiro was losing some health and also posture.
If this isn't working for you, then you can always try and burn him so his health lowers. That way, he will regain posture slower.
It also depends when you face him. I don't remember how powerful my attack was when I faced him and to be honest, I kinda flukilly beat him on my first try. There are so many paths you can take once you get to Ashina Castle so people's progression before the Genichiro fight may vary.