Mana regen runes seem like a huge waste to me. I can see the benefit of using Empower early, but I think leap strike and counterattack are much more useful. Counterattack at level 5 gives 18% dodge, you can get ~12% dodge from runes, with ninja tabi this amounts to about 40 dodge without having to get phantom dancer, although obviously that's a great item to get for the dodge, attack speed, etc.. but it is expensive, and you don't get the dodge until you get the phantom dancer (none of the build items have it). Warmogs is great for surviving but it's also very expensive, if anything I'd suggest getting regrowth pendant and either upgrading to philosophers stone early or upgrading it to a warmogs in the later game.
If you get nice dodge you don't need to worry too much about surviving for several reasons.. mainly because if you're dodging an attack, you're not taking the damage, you can also stun the enemy which gives you a chance to run off, and of course you get +10% move speed for 10 seconds after dodging an attack (with the mastery). At level 18 you get ~1900 health, if you get Phage thats just over 2k and with frozen mallet about 2600 - nowhere near as much as tank characters, but Jax has great DPS even without stacking damage items (although obviously because of his passive this is nice too).
A nice idea is to get cooldown reducing items - one that suits Jax perfectly IMO is Nashors Tooth, giving attack speed, AP (which works excellently with Jax), mana regen (with just 1 mana regen item, jax never has to worry about mana :P unless you constantly spam empower, but that's a waste of the skill) and 20% cooldown reduction. This means your leapstrike at level 5 is about 4 seconds cooldown, which is pretty badass, and your counter strike is less about 3 seconds.. meaning you can stun quicker and chase better