I started encountering the “Cannot connect to iTunes Store” error this weekend. There are lots of “remedies” on the Net, but this is the one that worked for me:
1. Open App Store
2. Go to Featured and scroll down to the very bottom. Your Apple ID will be displayed.
3. Tap your Apple ID and then tap Sign Out.
4. Open the Settings App
5. Scroll down to Store.
6. Tap Sign-in and then login with your Apple ID and password.
You should now be able to update apps. I also did a hard reset before I did all this, but I’m thinking it didn’t matter.
I got this from an Apple forum post though I tweak and simplified the procedure.