Skeleton Keys work the same way that The House of Wolves Treasure Keys work. You have the MAX 5 Keys? Yes, more keys can and will drop. NO, you can not pick them up unless you use one of your current 5. NO, they WILL NOT go to your postmaster, because you are limited to a maximum of 5. (20 in total, 5 per character and 5 in the vault) So use them shortly after you get them to avoid losing keys you could have acquired.
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As to why you lost the 5 in your inventory, I have no idea. I've only ever had 1 in my inventory at a time.