The phrase "against hope in hope" means hoping in the apparently impossible. Are you facing an "impossible" right now?
Abraham did not weaken in faith when he saw the utter impossiblity from man's viewpoint. Think about it. He was 100 years old. Sarah was barren. "Impossible" doesn't get any more impossible than that!
When I read about previous "heroes in the faith" in Scripture, I tend to find it even more difficult to be encouraged by their stories and God's dealings with them. After all, they are HEORES of the faith! How could I possibly compete?
It is important to remember that while the circumstances were different, they still doubted, became frustrated, lost hope and made huge mistakes. Specifically regarding Abraham in this situation, remember that he hoped BEFORE he saw a solution, BEFORE he saw or understood the HOW. God had promised him he would be a father of many nations--but this promise came BEFORE Isaac was born.
Do you see no way out right now? Do you see only closed doors? Do you feel forever locked in, with no way of escape? Good. Now look to Jesus. Look to the Author and Finisher of your faith. Look to Him Who created all and created you. He is infinitely capable to break prison doors, to free the captives and bring deliverance. But of much more paramount importance is you. He seeks to engineer your circumstances that you may know Him; to see Him despite the storm. He desires to strengthen your faith; to give you His hope; to give you His peace. He wants to shape you into a vessel which can reflect Him. When waves crash, when your life falls apart, when you lose all, can you see Him in the darkness? He could change your circumstances faster than you can even ask. But He desires that you learn to trust Him and rely on Him regardless of your circumstances.
Someone once asked George Mueller what the secret to a strong faith was. He answered, "The only way to know strong faith is to endure great trials. I have learned my faith by standing firm through severe testings."
If you are exhausted and wearied by the long trial; if you cannot even find the strength to look up to Him; He is yet near. Ask for His help to trust Him, to look to Him, to yield to Him and His purposes and ways.
I want to close with one more additional encouragement. Perhaps you do not find yourself in the midst of a great trial, but He is quiet. You pray, you read, you seek Him; yet He remains silent and seeminly aloof.
Consider Him and His character. Consider His past dealings in your life. Consider His faithfulness. Recall all of your answered prayers; the times He strengthened you and gave you His peace and hope. Has He changed?
L.B. Cowman wrote, "You must trust when all else fails."