Specific Swimming Technique Question: Body Roll

I'm improving my swim finally, but Im still pretty slow and tire easily.  One thing I noticed is when I start off, I have a good body roll which makes me feel like I'm just gliding through the water.....but after a while as I start to tire, I notice I'm really not rolling anymore (swimming with my belly button to the pool bottom).  I dont know if it's the lack of body roll that is making me get tired, or if my body roll is affected because I start getting tired.

Regardless, I started wondering just when I'm supposed to rotate.  I seem to remember reading somewhere that as you start pulling, your hip should turn up as your hand passes it, like your hand is pushing your hip up.  Is this correct? 

So once I have my right hand out in front of me, my left hip is up and belly button is facing the left wall, do I stay in that position until my left hand is out in front of me, or do I roll back with my belly button facing down as my left hand comes out of the water, or somewhere in between?  I guess my question is, do I try to keep my hips rotated as long as possible, or do I get my belly button facing the bottom sooner?