Her courage during her illness is an inspiration to us.
Literal
Illness-during [possessive-の] her courage [topic-は] us [for-にとって] encouragement [to-に] becomes.
病気中の ('during illness') uses 中 as a temporal suffix. にとって marks the perspective — 'for us.' 励みになる means 'to serve as encouragement.' A sentence expressing admiration.