Sustainable growth rate

Why sustainable growth holds only if assuming capital structure is constant?

Remember that the sustainable growth is defined as: g=bxROE

where b is the retention rate.

Depending on how much of you capital structure is equity, ROE will change and possible also b.

You mean ROE will change as capital structure changes?

Think of the DuPont formula for calculating ROE: increasing financial leverage, holding all else constant, will increase ROE.