At the Game Over screen press Up, Up, Down, Down, Button 2 to continue. You may do this three times.
Continue game play
Use controller two to bring a second player into the game when player one only has one life remaining. The game may be continued using player two after player one loses.
Errata
On Page 6, under "Continue Game", the manual indicates that if there are two players playing at the same time, a player will always be revived, as long as the other player remains alive.
This is not true. Once the two continues are used, the game ends, and the remaining player continues alone.