The sporty watch is, according to all the guides I've looked at, located at this canyon in Yaschas Massif 100AF. I've been there many times and tried everything: time reversal, blindly throwing Mog in, but the treasure box just isn't there! Its really annoying me coz if I get this one fragment from Yaschas Massif 10AF I can get 2 more fragment skills. I have finished the main story and a few paradox endings. Why isn't the treasure box there?
i believe it would be in 110af yaschas massif, from the ruins follow the path to the west(DO NOT GO SOUTH) till you see a canyon at you're right.
It should be in there(it's quite far away, i couldn't see it till had rown in mog).
If that doesn't work then you might want to try getting more fragments in the yaschas massif area. (since my second suspicion would be to much open quests open in the area).