The time for mincha is when dusk falls. It seems that everything is getting only darker, with no chance of light again. Yet, the work of creation also began at a time when everything was dark - and then came light! The time for mincha is a time of severe judgments, corresponding to the times in life when a person feels that there is no hope - that his evil characteristics are gaining the upper hand, and he has no chance of victory. But, the truth is that one can always call out to Hashem even then. The true tzaddikim, who labor constantly to reveal Godliness in the world, show that we always have the abililty to seek Hashem.