The enemy wins because he attacks your ships one at a time and is powerful enough that each shot kills one of your ships while your shots are partly deflected by his defenses causing minor damage. You run out of ships before he runs out of hit points.

Individually your ships are about 66s/8m attack 83s defense and 83 hp
His ship as you stated is 160s attack 200s defense and 113hp

As JMiddleton stated, his picking off a ship at a time while weathering your overall attacks. As the battle goes one, he's becoming more and more invincible. DA changed the way the battles are done and thus in the instance you have...1 ship will stomp 6 in DA when in DL that solo ship would have been crushed.

There is a thread around here arguing the point that Logistics works against you now in DA/TA for this reason.

Also, was it every shot at you or just every round that defenses were replenished?

I started with DA, and it all made sense to me. If you battle multiple ships you see what is happening. The defense of the ships is the key - as well as the overall hit points. Take two ships with 50 Attack in one fleet, and then 10 ships with 20 Attack in another fleet, and then put them into combat. The 10 ship fleet will win (depending on total hit points). Once you add the defense factor, however, things change. Same scenario, but have two ships 50 Attack and 50 Defense, and then 10 ships with 20 Attack and 20 Defense. This time, the 2 ship fleet will trounce the other fleet. If you look at each ship individually, if a 20 Attack goes against a 50 Defense, the majority of the time, no damage gets through the defense - as it should be. This design allows defenses (and the proper type of defenses) to become an important and realistic factor in your ship designs. Also, for Twilight of the Arnor, it adds importance to those techs that are Fleet related techs. It is NOT automatic that 10 weak lasers fired independantly from 10 different ships from different directions at a single object will perfectly time themselves to fire at the same time, hit the same location, and have their magnitudes add up perfectly with each other to equal a more powerful laser 10x the power. Make sense?