During gameplay with several users, I was using version 1.8 of minecraft. I was able to pick the item successfully from the item frame, but they were not.
All the NBT data associated with the item was erased. Updating to Minecraft 1.8.1, then 1.8.2, then 1.8.3 and 1.8.4 all gave the same result, an inability to pick the block.

The Mineplex server's creative has a large group of interesting and cheaty items, all using the NBT tags of items, and I was attempting to showcase the ones I'd gathered on my wall.

To recreate the problem:
1. Place an item frame on a wall
2. Get an item with NBT data (ie. an enchanted item or custom potion, a renamed item, etc.)
3. Place the item into the frame
4. Use the Pick Block key on the item frame
The item the Pick block function creates is a generic version of the item put in, with the only thing retained being the metadata.