1
general::
Phrase(s): hope against (all) hope
to have hope even when the situation appears to be hopeless. • We hope against all hope that she’ll see the right thing to do and do it. • There is little point in hoping against hope, except that it makes you feel better.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Hope or wish for with little reason or justification, as in I'm hoping against hope that someone will return my wallet. This expression, based on the biblical "Who against hope believed in hope" (Romans 4:18), was first recorded in 1813.
American Heritage Idioms