The White Army failed to overthrow the Bolsheviks mainly because the Bolsheviks received support from the working class of central Asia. While the Bolsheviks had Lenin as their leader, no one person was in charge of the White Army.
The Whites had several leaders – Yudenich, Deniken, Wrangel and Kolchak. All of them wanted glory for themselves; they fought differently without co-operation which made it easier for the Bolsheviks to defeat them individually.
Also, the Bolsheviks were fighting for a definite cause (the establishment and survival of a communist Russia) but the Whites had problems motivating their troops and building up support. Some Russians feared that foreign intervention might bring an end to Russian independence in the case of White victory.
Over time, many soldiers deserted the White Army; it wasn’t surprising to see the Bolshevik support increase dramatically given the choice between them and the Whites.