is this because of how long they are  admiring the same items, or tied to the item rarity, or totally random?

Yes, admiring has diminishing returns and they will eventually be bored of looking at the item. It resets every hour or so I believe, so they won't be bored of their items forever. Mini's also have hidden items they like more than others. You may find an item your Mini loves (heart bubble) and that will give you the most inspiration!