Look at it this way: reason and basis are synonyms in that both pertain to what underlies or supports. A reason can be described as a basis or motive for an action; however, a basis isn't a "justifiable" reason. It's the fundamental assumption(s) underlying an explanation. Failing health is neither a fundamental principle nor an underlying concept.
Originally Posted by queenbu
Yet another dictionary:
SYNONYMS basis, ground. These nouns pertain to what underlies and supports.
Basis is used in a nonphysical sense:“Healthy scepticism is the basis of all accurate observation” (Arthur Conan Doyle).
Ground is used figuratively in the plural to mean a justifiable reason: grounds for divorce.