Based on Bhagavad Gita Chapter 09, Text 30
Falling down means that due to our past conditionings or present circumstances, we succumb to temptation.
In contrast, falling away means that we give up devotional service and go away from Krishna.
Falling down is something akin to a child’s falling while learning to walk. It’s undesirable, but it’s often unavoidable — that’s just the way learning usually happens.
Nothing can make us fall away except ourselves. Temptations can make us fall down but not fall away. Why not? Because temptations don’t keep us in their grip all the time. They come, they make us fall, and then their madness subsides.
What we do at this point is critical. If we keep contemplating on the temptation, we may become agitated for another round of indulgence. Or we may become discouraged and not even try to take shelter of Krishna, thereby making ourselves vulnerable to future temptations and the resulting falls. Either way, contemplation on the temptation causes falling down to degenerate into falling away.