I hope I'm not jumping the gun, but after having the same "No Sim Card" problem, trying the various "fixes" ... removing and replacing Sim Card, turning Airport Mode off and on, etc., without a permanent fix, just now I removed the Sim Card and cleaned the inside of the Sim Card slot on my iPad2. To do this I took a thin flexible piece of plastic (it's actually one of the collar stiffeners from a men's dress shirt, but a strip of cardboard would also work. I folded a cut to fit strip of paper towel ( I used heavy duty Bounty paper towel so it wouldn't fall apart ... a piece of clean cotton would work as well) over the plastic strip, soaked it with isopropyl alcohol, and carefully slid it back and forth in the slot a couple of times.
Then I reinserted the sim card and turned the iPad back on. At first I got the no card message again, but after simply turning Airport mode off and on, then wi-fi off and on, it started working again. This was a few hours ago. I've gone back to the iPad several times now and when I've turned it on, it continues to work properly. Only time will tell if this will work, but since I've had the no card message non-stop for 2 weeks now, it's definitely encouraging.
It makes sense, because one of the fixes was to clean the Sim Card. Why wouldn't the Sim Card's receptacle be just as likely to get dirty or have a tiny bit of dust on it, stopping the connection. Wish me luck.