Your balance doesn't stay steady throughout your life. Just like your muscles and bones, your steadiness can deteriorate if it is not maintained. However, balance training isn't part of most workouts.
As you get older, the senses involved with balance can start to dull -- vision and your ability to sense touch, temperature, pressure and proprioception (your sense of where your body is and how it moves.) However, your balance can be shored up, even in very old age.
According to the Los Angeles Times:
"A 2007 study ... looked at the effect of a yearlong balance training program on women with osteoporosis. By the end of the study, the women's functional and static balance improved, as did mobility. Falling frequency declined ... Balance training almost always involves targeting core muscles -- the ones surrounding the trunk and the back, such as the abdominals, obliques and latissimus dorsi."