The exact example I am using is a Headband of Vast Intelligence and the spell Fox's Cunning and the headband and Crimson Sphere Ioun Stone
Both combinations grant an enhancement bonus thus normally wouldn't stack. However after 24 hours the Headband's bonus becomes a permanent bonus as long as it is not removed.
Does this change the bonus the headband grants in anyway to allow the other spell/item to also grant the bonus or does it still count as an enhancement bonus meaning the others cannot stack?
Best Answer
The enhancement bonus part does not stack with the other spells or items. Whichever bonus is the largest at the time is the one used.
No matter if the enhancement bonus from the headband is being used or not, the skill bonus from the headband persist so long as the headband is worn.
So even if you have a +4 from a Fox's cunning spell, you would still get the skill bonus from the +2 Headband even if you are not getting the +2 INT from the headband.
Also, despite the bonus to INT being permanent after 24 hours, skill ranks are not increased retroactively. http://paizo.com/paizo/faq/v5748nruor1fm#v5748eaic9og7