It took me many months to get up to swimming even 300m non-stop. After 10 months I can now go to 1000m but I'm still fighting sinking hips. I just read that doing side swimming drills can be a good way to learn better balance and help correct this.
12x25's kicking on your side.
With your hips rotated to the side, and your shoulders parallel, keep your head still and continue looking at the bottom of the pool. Extend one arm out in front. When you need air, rotate all the way onto your back, take a few good breaths, and repeat. Do odd number lengths on the right side, even lengths on the left. Now you're getting the feeling of being on your side in the water!
I'm going to try this tomorrow for the first time.