I have the same issue with my Griffin Defender case. There is no physical way to grab control center while in the case. Adding a milimeter or two to the grab area would easily absolve the problem. I'm also guessing there's a different grab area than notifications center, which still works fine in the case.
I have an Otterbox Defender case as well and here's my advice that I learned after fiddling with this **** thing all day... Place your finger at the very bottom of the case, where the case and screen meet, and with just the smallest part of your finger making contact with the bottom most portion of the screen, at the lowest point possible on the screen, swipe up. Hope this helped and didn't sound too ridiculous. It took awhile for me to master, I can tell you that!
I have same problem with a Lunatik Taktik Extreme case on my iPhone 5, just can't grab that **** bar. And to those who say its 'our fault' for buying a bulky case thats just rubbish, Firstly, the case is over $100 and I purchased it to guarantee protection of my phone so I will not simply not use it, second, these bigger protective cases were out prior to iOS 7 was released.
The top notifications bar works fine but grabbing the control centre is impossible. A few millimetres increase to the grab area would be perfect. Also to note as well is I get occasional lag when grabbing the bar without the case on.
With the Otterbox case, the way the plastic around the button sticks up further than the rest of the bezel, try grabbing the control center from either bottom corner of the screen. More surface of your finger touches the screen there. I've had far more success this way. I still agree they need to make the active area a touch bigger though.