I hope against hope that my lost cat returns home.
hope against hope
idiomTo continue to hope, even when what is hoped for seems unlikely or impossible.
Origin
disputed originLikely a paraphrase of the first few words of Romans 4:18.
Even though the doctors said the treatment might not work, the family continued to hope against hope for a miracle.
Despite the overwhelming evidence that the business would fail, the founder chose to hope against hope, pouring his remaining savings into one final, desperate attempt to save the company.