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BBT is right.
CRB Ability Score Bonuses wrote:
Permanent Bonuses: Ability bonuses with a duration greater than 1 day actually increase the relevant ability score after 24 hours. Modify all skills and statistics related to that ability. This might cause you to gain skill points, hit points, and other bonuses. These bonuses should be noted separately in case they are removed.
CRB Feats wrote:
Prerequisites
Some feats have prerequisites. Your character must have the indicated ability score, class feature, feat, skill, base attack bonus, or other quality designated in order to select or use that feat. A character can gain a feat at the same level at which he gains the prerequisite.A character can't use a feat if he loses a prerequisite, but he does not lose the feat itself. If, at a later time, he regains the lost prerequisite, he immediately regains full use of the feat that prerequisite enables.

Ciaran Barnes |

If the feat is granted by a class feature that says you gain the feat even if you do not meet the prerequisites (or that you can ignore the prerequisites, etc), then you can still use it even if your Intelligence drops.
Oh, and Intelligence is properly called an ability score. In Pathfinder, a stat block is a condensed collection of all of a creature's capabilities, not just ability scores.