They will get off the bus when they are replaced by a transaction that paid a higher fee, or if a miner decides to not include that transaction in a block for whatever reason.
If they disappear it means that they have been deleted from your browser's memory, either because the "Max Txs In Memory" setting has been hit, or because the transaction was dropped.
That is something to think about! I do plan on turning this into an interactive dapp game down the road. If any devs are interested in working on this with me, please contact me on twitter or telegram.