I was running the raid yesterday on my Warlock, and we got to Aksis, which I had already completed on my Warlock. Without thinking, I changed characters and completed the raid. Being late, I went to orbit, then quit the game, then shut down my console. Maybe 20 minutes later, before heading to bed, I was checking Destiny Item Manager on my phone to see what loot went to the Postmaster when I saw 3 Siva Key Fragments sitting in my Warlock's Postmaster. Remembering that people think quitting the game with fragments in your Postmaster causes your inventory of fragments to disappear, I moved 60 of the 63 fragments on my Warlock to my Titan using DIM, leaving 3 in my Warlock's inventory and 3 in my Warlock's Postmaster. Today, I'd forgotten about this issue and booted up Destiny along with DIM on my laptop. DIM had loaded around the time I was at the character select screen in game, and it showed no Siva fragments in either my Warlock's inventory or Postmaster. Sure enough, I picked my Warlock and they were gone. Thanks to this subreddit, I knew enough to move my fragments and save 60 of them (the extra 3 I left in inventory were a sacrifice for science). I was able to move them probably 20 minutes after quitting the game and shutting down my console. I don't know if I would've been able to save them today or not, but if you think you're in trouble, give an item manager a check before logging back into Destiny.
tl;dr If you think you might have Siva Fragments in your Postmaster after you've already quit Destiny, try to move the inventory from your character using an online item manager before logging back in; it might save you half a dozen keys.