How do I pray when the doctors give no hope?

You are allowed to ask for the very thing they call impossible. Prayer is not a forecast, and honesty before God is not disloyalty to the doctors. Ask for it — and ask, too, for strength for whatever comes, and mercy within it. Many people find they can hold both at once, and that holding both is what keeps them standing.

The tradition calls this bitachon — trust: not the certainty that it will go your way, but that you are not carrying it alone.

From the sources “The Lord is near to the broken-hearted.” — Psalm 34