Is there any party who is archiving all transactions that have been broadcast? There is a person claiming that Blockchain.info/wallet sent a transaction but for whatever reason that transaction never got included in a block.

If the transaction is valid today but perhaps just didn't get re-broadcast for whatever reason and has since expired from each node's memory pool, any party  with an archive of transactions could re-broadcast that transaction and it now might get included in a block.

Does anyone maintain an archive of all transactions, for instance, by archiving each OnTransaction event in BitcoinJ?
Anybody that has downloaded the blockchain has a log of all transactions. Blockchain.info should have it. In the future only accept confirmed transactions