The squeaky wheel receives the grease is a rather famous proverb. As a child I can remember riding with my family for long distances in the family car, and the squeaky sounds of the wheels drew attention to the need for lubrication.
God is not an unjust judge who must be harassed before He responds to us. He is our loving Father who really cares and hears us when we cry out to Him. Regular, persistent prayer draws us closer to Him. It may appear that we are a squeaky wheel, but the Lord welcomes our prayers and encourages us to approach Him with our petitions.
As Jesus instructs in the scriptures, constant prayer doesn't require long periods of "vain repetitions." Instead, as we bring our needs to God "night and day" and walk with the One who already knows our needs, we will learn to trust God and wait for His response.