My feeling is "rest" is correct, rather than "rests" but when "their" is used, I think it should follow by plural form. But how to explain to learners?
They have earned enough for their rest of life
They have earned enough for their rests of life
Those sentences are both wrong. It should be: They have earned enough for the rest of their lives. "rest" in the sense of "remainder" does not have a plural.
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Those sentences are both wrong. It should be:
They have earned enough for the rest of their lives.
"rest" in the sense of "remainder" does not have a plural.