How do I NOT DIE?! Jax Vs Kennen

I can't not die as jax versus kennen.

It started out great. I got a kill on kennen, or rather my did and I got an assist, and I ended up staying in lane, getting bullied out by being Q'd after he speeds around my minions and Q's me with his big minion wave, which either forces me to jump back or take harass. I go back, start building my BoRK, and head back to lane. Eventually I get bullied out again, 70% health remains, and I'm standing far behind my minions. He rushes forward, Shurikens, stuns, and autos me. I'm now very low. Under tower, I get dove and die. The process repeats with more tower dives.

How do I NOT DIE!?

This makes me mad because I thought if I simply played safe that I wouldn't die. Hell, I even got a gank early and I still ended up getting destroyed.

I was playing extremely safe, more safe than I ever usually am. Of course i took some free harass getting some cs, but what got me is when he just went at me when I wasn't even csing.