My first impression was that you made a very poor choice of words. And the question itself is incoherent. Put down to death? I am also from Asia and I have no knowledge of girls put down to death just based on gender. If you are referring to killing of fetus after sex discrimination, yes that may still exist in some parts of Asia where giving birth to a boy is preferred over giving birth to a girl. However, making a general claim that girls are put down to death just based on gender is a vaguely inappropriate and misleading statement.
I agree with Pradeep Baral, we need to be more precise in the definitions. One issue, as he says is abortion after in utero sex section tests. But female infanticide and neglect leading to death of female babies and toddlers does seem to exist, at least very recently. The clearest evidence is for India and China where the male/female ratios are significantly different from those in other countries. The former one-child Policy in China surely affected this behavior in China. The evidence in China and India doesn’t preclude the existence of the practice in other countries with strong preferences or needs for male children.
As Erica Terranova says, the reasons can be many and are related to sociocultural, legal, political, and economic factors that can be country or region specific. Regardless, general empowerment of women, starting with education, can be a good place to start. But China is a good example of a sweeping policy change that can also alter a direct, though not underlying, motivation to effect great change.