I believe that all of your belongings are ALWAYS supposed to be within your sight while they are doing security inspections on you or any of your other belongings. You can insist on this. While it may take a few moments longer for them to collect all your items and bring them to your search area, it is worthwhile, IMHO.

As for your Continetal Elite status, that holds no water what so ever with the TSA folks, nor does CO have anything to say about their inspections. The government barely allows the airlines to control the lines up to the security check points, but they have nothing at all to say about the method or manner in which the inspections are handled.

Good luck and congratulations on your first child!