I have just created this account to tell you that nothing would change if you restored your phone.
The first NO SIM nuisance happened just a week ago. Nothing had been done to the phone before that. I pressed HOME + POWER buttons to restart the phone and SIM card was successfully recognized as if nothing had happened. Then I had a lucky week, not reminded of this issue at all.
Today, however, the same problem keeps annoying me. I've used the same method to heal the phone but all I have done seems more like a placebo. So I tried the ultimate solution, restroing it in iTunes.
Ridicuously, the moment I finished basic setup on the newly restored phone, the same NO SIM CARD INSTALLED message poped up.
So IMO, it's not what you should do to erase and restore your phone.
Plus, I called my native carrier and they said no such problems have been submitted. And since my nano SIM card is quite new (three months old), I'm not going to replace it.
I googled this problem and found something on a Hong Kong webpage. The author of that thread points out that there is a flaw in the SIM card tray that prevents the phone from successfully recognizing SIM cards.
And I really hope Apple could probe into this issue and give official solutions other than restarting / restoring the phone like an idiot.