I just had the same problem with my iPad with the same message. Found your post and also powered down the iPad, unplugged the USB (which goes into a hub), then plugged the USB back, and the iPad started and was again recognized by iTunes. I also don't get the message Trust this computer? My iPod didn't have this problem. Thanks for the tip. (I use a Macbook with Snow Leopard and haven't had this happen before.)
I had the same problem, but with my iPhone 5. My iPhone and my MacBookPro are completely up to date with software updates. I had the "Trust this computer" message and everything, but my iPhone also stopped connecting to the internet. It said it was connected, but I couldn't access anything on the internet or through apps that required an internet connection. While I was having this problem I was able to connect to iPhoto, and I used the cable with other devices so it clearly wasn't the cable.
I did what you said. I turned it off, unplugged all the cables, turned it back on, and plugged it in and it worked.
But why did this happen?
Is there a problem with iTunes? Or is it our devices?
I hope we get an answer soon.
I have been having the same problem. I can not connect to the internet. It tells me that the server is unavaialable or something to that affect. Also, I went to plug my iphone 5 into the computer to see if I can reset it to get the thing working correctly again, and it said iTunes could not connect to this iPhone. Could not connect to this device. It would not connect to safari, update facebook or twitter and every time I went to get my gmail, it said can not get mail - about 4 times a window would pop up, but it did get my mail. Very frustrating. I just unplugged it and shut the phone down, turned it on and it works. I am assuming that it may be an issue with apple but hopefully they can fix it. I don't want to keep doing this and like to be able to connect to the internet whenever I want.