I feel consistently like I'm dealing enough DPS as an AP champ, but the fall-off still happens due to durability and sticking power. If you can't live long enough to land a couple spells, the general pattern is that you of course will fall off. The sticking power point is that other items scale too well. ADCs who can out-lifesteal a 1k nuke is definitely a concern.
Shields and health are particularly more of a counter for AP mages in a sense, because a nuke will deal "X" damage (reduced by MR). It then has to wait to be cast again. That wait period in early-to-mid game is a bit more consistent with the dps you need/want to be dealing, maybe not game-breaking, but certainly impacting. A 500 damage nuke on a 6 second cooldown sounds hefty, but the rate of fire means if it doesn't kill, the enemy can then retaliate, regenerate, mitigate and/or retreat. It's not that you're looking for an assassin pattern of a fast kill, but you certainly want to be able to hit again and actually kill on the 2nd or 3rd set of output you dish out. This doesn't happen so fluidly.
You consider the various roles you are fighting based on itemization...
ADC:
+ 
(2 shields and silly sustain piled on top of DPS.)
Tank:
+ now: 
and/or 
Assassin:
+
(Bruisers/Juggernauts fall into a hybrid-class of a few of the above, usually using the same items.)
Supports and Mages generally are your prime targets since they ideally are the targets on level footing. The items they have available are the same ones you probably can get to counter them. Which is really troublesome since that line is foggy for those 2 roles. Yet it's more I find that the means to counter the other types of enemies are insufficient, rather than the fact that they can counter-build you.
If you counter-build an ADC as an AP caster:
If you counter-build a tank as an AP caster:
An Assassin?
or 
It's weird, because health is the counter-all. So Rylai's, RoA, GLP and Protobelt provide in that regard, but the more you analyze it's not quite the same efficiency as other roles have. Zhonya's doesn't really compel consistent engagement, more of an "oh crap" button than anything. You get a couple seconds on your cooldowns, but generally are put sitting duck. Boots? As a counter, they aren't really the most efficient choice, but sometimes you just have to. Liandry's makes for health melting goodness, but as a DoT you both need the magic pen and the CC through probably rylai's to make it count all while giving up sustain that other classes don't.
is a weird one. It technically has more gold value than a Deathcap. Think about that for a second. It's dps-granting powers come from the Magic Pen which allows you to hit closer to the true dps-value of a spell. Your spell can read that it will deal 500 damage, but 100 MR will make that deal 250 damage without MPen. Void staff mitigates the effects of MR in this sense.
The only items I can 100% say work in a sense are Luden's and Morello's. One gives base power combined with utility of a splash to a spell and the other gives enough base stats to keep someone running for a while before you even consider the passive, which is necessary to counter a heal-based player, but also relies on a health threshold that people can sometimes avoid dropping below. (Though it wouldn't necessarily be fair or balanced if it was applied before the current threshhold.)
It's not easy to explain exactly what's wrong with itemization for mages, but here's the core points:
- Utility. Uniques abilities items have, need to work for intended use or have an additional use to begin with.
- Sustain/Durability. AP caster items lack a certain edge if you're looking for it.
- Synergy. If you analyze what works about the items other classes use, you'll notice a lot more effects on items that kinda chain together. Synergy as a point is a weird one though. It's not that all the items don't have a certain synergy individually, only that the total composite effects could use some work, so that a complete item has more impact than buying a similarly priced component item.
Frontline
Backline
Manaless
but again that's going to be determined by your champion based on their ratios and play pattern. It really doesn't vary based on what is happening ingame.
)
Adjust AP ratios on all champions to use Base/Bonus/Total. Mostly this would differentiate the mage subclasses, and have little effect on champions who don't actually buy AP.
Would also help to stop some Mages from being nerfed into Support (likely not enough on it's own though).
has 0 AP at level 18. So much untapped power eh?
and 
hurts man
depending if the mage has burst or cc.
Assassins have 