I also have this problem. It says to check my network connections. But all is fine there. I even disconnected from my home network and connected using my cellular data network and get the same thing. I'm also having a similar problem with iPhoto when attempting to use its sharing features. It says No Network Connection. This has been going on for months and at one point during that time, both problems cleared for a very short time but are now back. I'm completely stummped.
I do not know if you have this solved but I may have a solution. I have a MacBookPro early 2011 model with iTunes 11 installed. This is what I did to get it working;
1. Close iTunes
2. Open System Preferences
3. Clicked on Network
4. Select WiFi in the white column on the left
5. Choose the Advanced button in the lower right hand side
6. Press the Proxies tab
7. Choose Auto Proxy Discovery (a tick will apear)
8. Press Ok, then Apply on the Network section and close the window.
9. Relaunch iTunes and see if it connects
Hopefully it works for you.