I'm not sure if I would consider ceasing an attack then attacking the same place to really be ceasing the attack.
Perhaps this example will help:
Let's say you have a bunch of dudes in Brazil. You could throw the dice against Argentina, and if you didn't wipe out Argentina, switch and attack Peru. After the attack from Brazil to Peru, you could switch back to Argentina and repeat as often as the attacker wishes.
If the attack on Argentina wiped opposing troops out, you'd have to move in some dudes from Brazil. If this move results in more than one dude in each of Brazil and Argentina, then you can choose to attack Peru with either your Brazil forces or the Argentinean armies. The aggressor would have to choose to attack from either Brazil or Argentina. After each throw of the dice, the player has the option to stop the attack from one territory and start a new attack from the other territory.
Perhaps this example will help:
Let's say you have a bunch of dudes in Brazil. You could throw the dice against Argentina, and if you didn't wipe out Argentina, switch and attack Peru. After the attack from Brazil to Peru, you could switch back to Argentina and repeat as often as the attacker wishes.
If the attack on Argentina wiped opposing troops out, you'd have to move in some dudes from Brazil. If this move results in more than one dude in each of Brazil and Argentina, then you can choose to attack Peru with either your Brazil forces or the Argentinean armies. The aggressor would have to choose to attack from either Brazil or Argentina. After each throw of the dice, the player has the option to stop the attack from one territory and start a new attack from the other territory.