The two reasons an appraiser wouldnt take a collectable is that its the wrong type(a quest or custom delivery collectable attempting to be handed in at a scrip appraiser), or because you didnt raise the rating over the minimum to turn in. Try to focus on the "rarefied" items unless a quest or NPC specifically asks for something else. And if you do end up with some collectables you cant turn in, i believe you can right click them and select "lower quality" to turn them into "normal" items that you can then stack and potentially vendor off.