David Wilkerson emphasizes that there are moments in life when situations become utterly hopeless, requiring a miracle that only Jesus can provide. He illustrates this through the story of a nobleman whose son was gravely ill, highlighting the father's determination to reach Jesus for help. The nobleman's faith was tested, as Jesus pointed out that belief in Him was more crucial than merely witnessing miracles. Ultimately, the nobleman's faith led to the healing of his son, demonstrating that true hope lies in trusting Jesus as the source of life and salvation.