。
The strain started to take a toll on his body.
Literal
Unreasonable [subject-が] his [possessive-の] body [to-に] respond begin.
こたえる (応える) here means 'to affect, to take a toll on' — a specialized sense distinct from the 'respond' meaning. ~始める ('begin to') as a compound auxiliary attached to the verb stem. 'Strain began to affect the body' = 'started wearing him down.'