I've got the same problem - when i' trying to delete app and pressing x at the left corner - iphone doesn't even ask me about deleting andafter about two minutes restarts.
What is the reason?
I've got this problem on iOs 6, i upgraded to iOs 6.0.1 but the problem persists.
It will ask you if you're sure you want to delete it.
Same thing happened to a family member, but it worked when I tried for them. Try tapping a little bit higher, or if you have one try using a stylus. The x is pretty small.
Meadiasteven, Thank you!
I assure you I've deleted a lot of apps and aimed correctly :)
And I know about the other way of app deleting.
Anyway I've solved the problem by restoring the default settings. And now I can delete apps as earlier.