How did you generate your paper wallet? And what do you mean by "accessible on the Blockchain"? Do you mean you see transactions being sent to your paper wallet?
I generated it on the blockchain and printed it out.
I guess what I mean by accessible is that I'm still able to move coins from wallet to wallet when I log into my wallet on the blockchain.
That isn't a paper wallet. Not sure what you did or think you did but you didn't create a paper wallet.
A paper wallet is ONLY offline. It doesn't exist ANYWHERE else.