Reading aloud one evening, my wife pronounced indefatigable as in-de-fa-TEEG-a-ble -- quite on the measure of British class-i-fi-CATE-or-ee. I personally say in-de-FAT-ig-a-ble; but that is morphosemantically opaque, whereas her version nicely brings out the notional relation to fatigue (with its French-derived oxytone). Might this be another case where the Brits displace the accent? But no, according to the dictionaries, no; she came up with it on her own hook.
[Note: The above is an update to a more extensive essay, here.]