I have my doubts about cherishing hope. One may cherish many things, meaning that one holds them dear, puts great value on them, thinks of them fondly, but hope? One harbors, entertains, clings to, or holds out hope.
The Oxford English Dictionary seems to disagree with me, acknowledging the cherishing of hope: "To entertain in the mind, harbour fondly, encourage, cling to (a hope, feeling, design, etc.)" noting that this is "The most frequent current sense."
I still don't like it, because the original and most persistent meaning has always been holding something dear, but I have to admit it's a pesonal preference.