When dealing with an AP hero's balance you have to look at each hero individually. A blanket statement like "ALL AP IS UNDER POWERED" May not be true for every hero, and figuring out which hero's are AP hero's and not hybrids can be a little tricky as well. So I'm just going to talking about something that all AP hero's will have to get around.
We all know the meta game right now is very tanky. Hero's like renekton, amumu, shen and rammus are shinning. The ability to soak tons of damage while doing medium damage allows them to beat you by enduring. So this means that AP hero's have to counter specific situations. For example, if I'm playing a traditional caster like ryze and i see a team full of hp stacker's. I will probably reach for a death chill. But the death chill is not as good of an item as its AD brother mandread razor. How about stacking straight AP? Well i guess that helps the damage but now your getting rofl stomped because your a glass cannon. That's just one situation, another issue i have to raise is the strength of magic resist items opposed to armour items. Lets ignore for now the token MR items like chalice and focus exclusively on B veil and force of nature. Now your a caster and you see a B veil. How do you counter it? Magic pen. Well that works for the static magic resist but not the passive spell block. And force of nature provides alot of HP regen and MR and even movement speed for the tank its a no brainer to take it. So this forced the caster to stack tons of magic pen just to compete against the enemy. Its annoying and hard to get around when playing AP and i hope it gets resolved considering there are not as many fun AD character then AP characters.