Does the word “indefatigable” have positive or negative connotation?

Question

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.

Answer 1

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.

Answer 2

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