"How long will the card hold the IP address set using NetEdit3 if the card is removed from the PLC and put on the shelf?"
It is stored in flash... so, practically speaking, forever.
"Is there any chance any of the settings can be corrupted going through an airport scanner?"
Of course, just like your laptop. That possibility is remote, but nonetheless real. When I traveled a lot for field service, I always backed up my laptop beforehand. The thing with ECOM100s, however, is that there are not really that many settings. And there is no way to back them up anyway. But the X-rays are not powerful enough usually to do anything as I have never had my laptop compromised by them. The dangerous part, however, is a metal detector, or a metal-detector wand that the guards carry. Those generate magnetic waves that can erase hard drives, and possibly modify data in memory.