What would be the reason that a born again person would fail to confess a sin? It would be like a person with greasy hands standing in front of a sink with hot water and a bar of Lava and refusing to wash. It would make no since. We believe this is why First John can say on the one hand that a born again person does not contiunually sin and on the other tell of God's provision for sin: confession. The born again keeps himslef from sin by confessing it whenever he sins.
The bottom line is this: unforgiven sin must be judged. Therefore, the answer to your question is yes, one unconfessed sin can result in a person being cast into the lake of fire.