When is it permissible for a sick person to pray sitting down, even if he is able to stand with extreme difficulty?

Standing is a pillar of the obligatory prayer that is waived in case of inability. The Ummah has unanimously agreed that whoever is unable to stand in an obligatory prayer should pray sitting, and there is no need for repetition, nor is their reward diminished.

The criterion for the excuse that waives standing and permits praying the obligatory prayer sitting is: inability to stand, or an increase in illness, or a delay in recovery, or the presence of severe hardship that removes khushu' (devotional humility), such as dizziness for a person on a ship.

Indeed, Imran ibn Husain asked the Prophet, peace and blessings be upon him, about prayer, and he said: "Pray standing; if you are unable, then sitting; if you are unable, then on your side."

Complete inability is not a prerequisite for transitioning to sitting; rather, the presence of severe hardship, or the fear of increased illness, or perishing, or that standing would cause him hardship that removes his khushu', is sufficient.