I am constantly having issues claiming Prime Loot. I have been lucky lately, I guess, but I claimed this current one and did not receive my loot. There is something messed up with the linking between Prime and Bungie. I have linked/relinked which has not helped. I've missed several loot offers in the past thanks to this problem.
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Mine just dropped today. Check: https://www.bungie.net/7/en/codes/partners Mine shows [i]Prime Gaming Reward Offer 24[/i] as having dropped today, Jan 7th. Hope it's working for everyone else, too!