On Aug. 1, 2005, Square Enix implemented a patch that made a handful of NMs and HNMs grow significantly stronger after they have been claimed by players for a certain amount of time. This term has become known as Rage.
Attack, defense, and evasion increased. (It is virtually impossible to hit a raged monster. When hit, the attack usually does 0 damage except in the case of magic damage such as Mijin Gakure or Elemental Seal nukes.)
Monsters in this state hit for more damage (500-1000 when fully raged) and their attack speed is increased (comparable to a slow Hundred Fists).
Magic accuracy and accuracy are increased (King Arthro's "Waterga IV" spell will regularly hit for between 500 and 1000 damage).
Monsters in Rage status are generally considered unkillable because dealing damage to them is near impossible and they deal massive amounts of damage.
Rage status will only be removed by allowing the monster to become unclaimed and letting it restore itself to full HP and normal status.
The August 1, 2005 patch read as follows
The notorious monsters listed below will slowly grow in strength after a certain amount of time has passed since being claimed: King Arthro / Simurgh / Roc / Serket / Capricious Cassie /Lord of Onzozo / Behemoth / King Behemoth / Adamantoise / Aspidochelone / Fafnir / Nidhogg.
The time allotted to fight these Notorious Monsters before they enter Rage status has been listed below. (Some NMs other than those listed are capable of entering Rage.)