I think something that is often overlooked when it comes to keeping your hips up is mobility in the thoracic spine area and hip flexors coupled with solid core strength in the water. Basically having good posture. The major problem for triathletes especially is that both the bike and running cause these areas to get tight, and biking especially puts you in the opposite position required for swimming, with a hunched over back and shortened hip flexors.

Speaking from personal experience, I started working with a swim coach earlier this year, and sinking hips was one of the big things she had me work on. I did a lot of drills to work on it, coupled with building a stronger kick to support a better body position. I improved a bit going into the Oceanside 70.3, then I took a bit of a break from heavy running and cycling to focus on swimming. I improved a ton, I could feel my body position getting better and my times were dropping. But after one weekend with a four hour bike ride (much of it in the aero bars) and a 90 minute run, my swim form regressed back to pre-Oceanside. My hips and upper back were extremely tight, and that led to poor posture in the water and an inability to get my hips up high like I could before. And having fatigued legs made kicking harder as well.

So basically my advice would be to work on mobility, both in the water and out. Roll out your upper back, lats, glutes, and hip flexors. Strengthen your Psoas muscle and the muscles around your scapula. And do drills that work your posture in the water like side-kicking and 6 kick switch. And also do more kick sets to strengthen those muscles that help your kick. They do more than just propel you through the water.

(edit: exactly what Rwjohnson11 says above)

This goofy video demonstrates that it is the muscles that keep the legs at the surface. Although it is true that pushing down will tend to lower the legs, there is very little downward push in a normal stroke (unless you are doing Tarzan stroke). Are you suggesting that, say, doing a fist pull drill will cause the OP's legs to stay at the surface? What brings the legs down, then? I suggest that it is the "normal" position to have the legs *not* in line with the upper body, and that it takes an action to get them there. Cyclists/runners who spend an inordinate time in that closed hip position have tighter/stronger hip flexors that also inhibit the opening of the hip angle. That's certainly what I see in myself: work on hip flexor flexibility and my legs are more horizontal.

---

----------------------------------
"Go yell at an M&M"

Have a look under water at slower AOS swimmers in the pool. They ALL push the water down with their hands which causes the legs to sink.
My legs sink when I lay in the water horizontally. And as I wrote, only a very slight kick causes the legs to stay up. No further body muscles needed.
I stay with my theory.