We live in a world corrupted by sin. All things effected and affected by man have been corrupted and subject to decay, and this will not be reversed until Christ's return. As a result things fail. Quiet times are interrupted by thunderstorms or children waking up too early. Your car will fail when you need it to take you to church, or your ministry meetings/events.
If you determine yourself to not rely on external things you then put the onus upon yourself. If applied correctly this then has the affect of increasing your own personal drive. Your own desire to accomplish whatever the task is that God has placed before you. Instead of sitting back, waiting for someone, or something else, to step in and accomplish it, you are there and you are the one who takes action. And there are times when we even fail ourselves. It is especially in those times we can see, and feel, the grace and mercy of God.
In the end, rely on God for He is the only thing that will never fail.
But he said to me, “My grace is sufficient for you, for my power is made perfect in weakness.” Therefore I will boast all the more gladly of my weaknesses, so that the power of Christ may rest upon me. 10 For the sake of Christ, then, I am content with weaknesses, insults, hardships, persecutions, and calamities. For when I am weak, then I am strong. (2 Corinthians 12:9-10, ESV)