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Example usage:

Terence, you have indefatigable enthusiasm. The effect it has on people is inspiring.

In the sense of exuberance, but you feel positively about it.

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It just means tireless. Can tireless ever be negative? Yes. –  tchrist Feb 22 '13 at 14:24

2 Answers 2

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On its own: positive.

Modifying a neutral quality: positive.

However, it's not incorrect to use it as a modifier of a negative quality, so the obviously negative "your indefatigable stupidity continues to amaze me" is a valid use, too.

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Yes, indefatigable is a word with positive connotations (here). The repeated use of indefatigable as a warship name underlines the general tone of approval.

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I understand the idea of describing an inanimate object as indefatigable, but I was unsure whether it could positively describe a person's character. –  Ash Clarke Feb 22 '13 at 13:48
    
The OED has plenty of citations for indefatigable where it does not appear to have a particularly positive aspect. Yes, saying that someone is “tireless” does seem in general positive, but consider “relentless”. –  tchrist Feb 23 '13 at 1:20

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