Does missing one night of Ramadan prayer due to illness cause one to miss out entirely on the reward of forgiveness for having prayed the entire month of Ramadan, and can it be compensated for?

Whoever intended to perform the night prayer of Ramadan (definition) and was unable to do so due to a legitimate excuse—such as illness—will have the full reward of performing it written for them. This is because a Muslim has the reward of good deeds they intended written for them if they are unable to perform them. Scholars have based this on the saying of the Messenger of Allah, peace and blessings be upon him: "If a servant falls ill or travels, the like of what he used to do when he was a resident and healthy will be written for him."

As for making up for the missed night, jurists have discussed making up for the Tarawih prayer.