When can you do a replay? Well there is only 1 way to get one.

-When the MONSTER count on the opposing side of the field changes during Attack Declaration

If you declare an attack and the monster count on the opponent side changes (whether he gained a monster or lost a monster), you can either change your target or stop attacking.

Ex. of a replay
Player A has Magician Circle set and Ebon Magician Curran.
Player B has The Tricky face-up on the field.
Player B declares an with The Tricky and targets Ebon Magician Curran
Player A responds with Magician's Circle
Player A special summons White Magician Pikeru from the deck.
Player B chooses not to summon.
Since it is still attack declaration, replay occurs.
Player B declares an attack with The Tricky and changes its target to White Magician Pikeru

You CANNOT, I repeat, CANNOT resume attacking with a monster after you have chosen to not attack with it during replay.

Ex. of a wrong attack declaration
Player A Has Legendary Six Samurai - Kizan (1800 ATK/ 500DEF) and Legendary Six Samurai - Enishi (1700 ATK/ 700 DEF) on the field
Player B Has Call of the Haunted facedown and Elemental HERO Prisma (1700 ATK/1600 DEF)
Player A attacks with Legendary Six Samurai - Enishi directly
Player B responds with Call of the Haunted and targets Elemental HERO Prisma
Player A has no response and Elemental HERO Prisma is special summoned
(Replay)
Player A chooses not to continue with Legendary Six Samurai - Enishi
Player A attacks with Legendary Six Samurai - Kizan (Elemental HERO Prisma is destroyed)
Player A attacks directly again with Legendary Six Samurai - Enishi (WRONG!!!)

If you own monster count changes during your OWN attack declaration, you do not get a replay.

If a monster was destroyed by an effect during Damage Calculation, you do not get a replay because it is past Attack Declaration.

Ex. of a wrong replay
Player A has Ally of Justice Catastor
Player B has Elemental HERO the Shinning
Player A attacks Elemental HERO the Shinning with Ally of Justice Catastor (Right after Attack Declaraction is Damage Step, Ally of Justice automatically destroys Elemental HERO the Shinning)
Player A attack directly with the same Ally of Justice Catasor (WRONG!!!!)

If I missed anything, or if you have any questions or concerns, please reply to this post and I'll attend to it as soon as possible.