So, a little update regarding this situation. I brought it up to Nexon and they initially just told me that drops are random. I then highlighted the specific circumstances above, which elicited this reply:
Thank you for keeping in touch with us and …
If you have pet loot and a full inventory (whether it be pots,etc or whatever) I find it's causing constant d/cs. Fury increasing spawn means more loot, therefore more of a pronounced issue (I use frenzy). Try disabling pet loot and see if that fixe…
I'd also avoid collecting Familiars/badges. Keep the cards in your inventory until this issue is resolved, as I just lost a ton of progress (was testing it with easy to obtain cards to see how unstable/sensitive this issue is).