IOS – iPad frozen after long pressing an app icon

Since you've restored the iPad I would say that you've got some issue with the Hardware. If possible, Take it to an Apple Store for a Hardware test.

Using an app which requires the use of the Accelerometer may test it too.

EDITED: Its not the Gyroscope what tells the position of the device but the Accelerometer.

OK, I'm somewhat embarrassed, but it looks like the problem fixed itself after a couple of days. After noticing the issue first, it was reproducible for a couple of days. I backed up the iPad to iTunes, did a factory reset as a new device, and the issue was still there.

After that, I called Apple Support and they suggested replacing the device, since it seemed to be a hardware issue. I couldn't replace the iPad at this time since I was travelling, so I told them I would wait another couple of days.

When I was back from traveling, I backed up the device again and called Apple Support to arrange the pickup of the iPad. While on the phone with them, I had to describe the issue again and while doing so, was trying to replicate the issue while talking on the phone. Guess what, it worked this time and has worked now for the last couple of days without any issues.

I'm not sure how the issue fixed itself, but there are several possible explanations - not sure how reasonable they are, though:

• The iPad was with me on two atlantic flights (Europe - US and back), maybe the pressure change has fixed the issue, if it was a hardware issue. I remember that the issue was still there when I got to the US, but was gone after I got back.
• Doing another backup/sync with iTunes fixed the issue, which would mean that it was a software issue.

There may be other explanations that I don't see at the moment. While it all is a bit mysterious, I'm glad that it's working now. Let's just hope that it doesn't return.

Update July 2013

The problem returned after a couple of weeks. I finally called Apple Support and they exchanged the device for a new one, since mine was still under warranty. The new one works perfectly fine. So it looks like it was a hardware problem after all.