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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
up vote 3 down vote accepted

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
Though I agree it's largely positive, be wary using it with reference to a person's character, though, as the situation is much more complex there. – Dan Sheppard Aug 31 '14 at 20:30

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