Your comments

Any other ideas I can try?  Thanks.
Prahsant, 
Thanks for the reply.  Some answers to your questions:
1 - Based on other information on the SmartPlane site, I've tried keeping the iPhone very close to the cockpit.  I have run both sides of the iPhone as well as all four sides and four corners by the white cockpit.  Every part of the iPhone has been in contact with both sides of the white cockpit chip to no avail.
2- Yes, bluetooth is on (it never hurts to ask the obvious!!); the indicator is gray, unpaired with any other device, e.g., JamBox, headphones, or, most critically, the SmartPlane.
3- Turned off WiFi and repeated all steps of the pairing process.  No joy.
4- Yes, the plane is fully charged. It is flashing white at the speed of 1 flash per second.
5- As for bypassing the searching screen with a 2-finger tap, I had seen that suggestion before.  I did already bypass the searching screen to get to the app.  Sliding the throttle has no effect on the SmartPlane.  
6- I have tried all of the above steps with both my iPhone 5 as well as my son's iPhone 5.  Neither device pairs with the plane.

What I have right now is a fairly expensive, feather-light paperweight (...a poor attempt at humor).  Just trying to maintain a sense of perspective in all this!   
Just tried this.  iPhone 5 reset, black screen then Apple logo.  Started app, turned on plane, searching............     Still will not connect.  Tried having app open first then plane one as well as plane on first and then starting app.  No joy.   Would very much appreciate any other thoughts.  Thanks.