I have been having an issues with my iPod Touch 3g 64gb. The iTunes application icon is missing on the device and on iTunes. There are no restrictions on and I have tried toggling them on and off to no avail. If I search for it with spotlight I get it though. Also, I just did a restore on the device which took seven hours and that didn't even work.
Welcome to the discussions,
did you use all available screens on your ipod? If yes, there could be apps on your ipod no showing. To make them visible again, you'll have to delete some of the other apps on your device and they will be there again.
If you reset the home screen layout, you'll put all the original apps in their original locations, followed by third-party apps in alphabetical order. Search for Settings and select General > Reset and tap Reset Home Screen Layout. Maybe that will help you find it.
Of course, you'll have to spend some time to rearrange your apps again.