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So it says in the Intense Spells ability:
Whenever you cast an evocation spell that deals hit point damage, add 1/2 your wizard level to the damage (minimum +1). This bonus only applies once to a spell, not once per missile or ray, and cannot be split between multiple missiles or rays. This bonus damage is not increased by Empower Spell or similar effects. This damage is of the same type as the spell. At 20th level, whenever you cast an evocation spell you can roll twice to penetrate a creature’s spell resistance and take the better result.
What about damage over time spells or spells that require a chance to hit to do damage? Is it a one time additional damage or for each time it takes damage?
"This bonus only applies once to a spell"
So, for damage-over-time spells, it's a flat one-time bonus, presumably the first time the spell deals damage.
What about ... spells that require a chance to hit to do damage?
Mage's sword requires an attack roll to hit, so I'd rule it like a ray, which also requires an attack roll. The first attack carries the extra damage, and if the attack roll misses, it's lost.
I'd rule the other way for flaming sphere, however, since it's not an attack roll, but the target's saving throw. The first time the target is "hit" by the spell (even if they don't take damage due to things like energy resistance or evasion), that's when the intensified damage would apply.
My mind could be changed for any of these scenarios due to a precedent, but that's how I'd rule. Ultimately, intensified spells is a very minor damage boost, so as long as the clause I quoted at the beginning of this post is followed, any interpretation isn't going to make much difference.