Go barefoot more often
For you to have good balance, your feet need to be able to assume their natural shape. Wearing shoes conmpresses the feet. The bones are pushed together and the muscles and tendons get squeezed out of shape and can't fully function. The resulting effect is instability in your stance and your walk, which will also lead to problems of the ankles, knees and hips. Even flat sandals such as flip flops can cause some drag on the soles of the feet and result in restricted movement.
The solution: go barefoot when you can. When you get home from work, get out of your shoes and socks. If you have high atrches, you'll have to build a tolorance for being barefoot and you'll feel fatigue more quickly. You might need to put on your Birkenstocks or running shoes after you've been barefoot for a while.
Going barefoot will help most directly with standing balancing poses, but will help with all balancings, including handstands and arm balances. Tight muslces on one end of the body always affect the body elsewhere.
Learn to Fall
This is something I tell every Yoga client in every class, no matter what. I don't mean hold the pose until you fall over. What you need to do do is practice falling out of the pose-properly. Take a pose such as Salamba Sirsasana, or supported headstand.
The obvious, and sage advice, is to practice the pose on a wall. The wall will prevent a major accident; but many students become physically capable of getting into the pose and holding it without needing the wall, but hesitate to move away from it. The issue they have is that they have not intentionally tought themselves how to fall.
What one needs to do is practice repeatedly dropping the feet back to the floor-a.k.a. falling properly. Also, one must talk herself through the whole process of movement.
Talk yourself through the movement
Talking yourself through the process of moving into a balancing pose, and falling properly out of the pose isn't any different than doing so in any other pose. You move slow enough that your conscious mind, and your consious heart have time to "see" the movement by way of feeling it. Before even trying a balancing pose, take a moment in a more-basic pose, such as Virabhadrsana-Warrior pose.
In Warrior pose, we distribute our body weight between our feet by adjusting every muscle from the toes, ankles and legs to the torso, right up through our shoulders and arms.