Try to avoid singing with too "airy" or "breathy" a voice, even when singing quietly. This kind of sound can be desirable at times, but it also indicates that you are releasing a lot more air from your lungs than you could be. Experiment with singing with a more solid, or tight voice. This kind of singing is natural when singing loudly, but you can produce a similar tone at lower volumes as well. Doing this will conserve the air in your diaphragm and help you get through your entire scale.
If you are singing multiple octaves, are ascending and descending, or doing some kind of interval exercise that is longer than a simple scale in one direction, make breath marks on your sheet music; take advantage of these pauses in between notes to take short quick breaths.
Practice breathing exercises daily. These exercises will help you strengthen your diaphragm and surrounding muscles, which will help you breathe more efficiently. One simple breathing exercise is to inhale as much air as possible, and then exhale through your teeth to produce an "s" sound until you are completely out of air. First concentrate on keeping the "s" sound at a constant, moderate volume, and repeat multiple times. Then do the same thing at a higher volume. This sound will be harder for you to sustain, but if you repeat it daily, you will be able to sustain it for longer.