I've had a quite a few people contact me of the the years with similar ideas/problems. Different causes, for example in the past I have talked to people that have had strokes which caused balance problems. Cutting a long story short what you ask is feasible. In fact it is practical to do and in recent years the cost and performance of the sensors have improved. It is also worth noting that physical gyros (able to apply force) could be used as well as gyroscope sensors (sensors on a chip) to detect the angles of the body.
The bad news is no one has actually put everything together to do this. But the good news there is some research being done in this area. Two companies that I know about. I've helped one in the past and I'm helping another firm. Although in both cases the application is not quite what you want.
This is one of the firms http://gyrogear.co/gyroglove/
I'm somewhat stretched for time so couldn't start something else but my work is taking me closer to this anyway.
I have developed this item which is going on the market soon.
http://www.gyroscope.com/d.asp?product=GYROSTABILIZER
It appears to get close to close to the requirements of helping someone balance.