Vanishing Quest Items

I'm pretty sure it's to prevent people from gathering 20 days worth of items. It's also only the items directly required for quest completion that disappear, so if you keep both the roasted festival turkey and the festival turkey dish in your inventory, the dish will disappear the next day while the roasted turkey will stay.

An alt on Alexina has been at 3/4 Double Yolked Eggs for several days without them disappearing. Perhaps they only disappear when the quest is reissued?

Well yeah, stockpiling only works if you get the quest each day, which requires you to finish the quest sooner or later to get the next one.