That does sound like an odd problem... Maybe your hips are riding too low in the water? That could cause you to be too vertical and not horizontal enough and making you sink with every stroke. Have you tried doing breast stroke pull with a buoy? I also like doing breast stroke pull with a dolphin kick - it's fast and fun - but I don't know if that would help you, unless you can maintain a dolphin kick on the surface. Make sure you're also keeping your head still. You don't want to lift your head but rather shrug your shoulders up and keep your head in line with your spine as though you're walking upright.