I discovered that the flip control for connectors appears to function only when the connector is hosted to a face. I raised the issue at an AU session and several others confirmed by observation. The work-around when hosting to a work plane to ensure the connector faces the correct direction is to redraw the reference plane in a different direction. It corrects the problem but it is generally a very bad practice for many reasons. That connectors function this way is inconvenient, time consuming, counter-intuitive and silly. But that is not why I am posting.
Quite by accident, I discovered "the rest of the story."
I had a circumstance where the flip control did work correctly for a duct connector I had positioned with reference planes. Initially, I thought it worked because it was a duct and not a pipe and I had discovered the phenomenon for a pipe connector. This would have been odd at best but perhaps that is what I saw. I tested my theory and placed a new duct connector hosted to a reference plane and this time, the flip control did not work. Huh?
What I finally discovered after wasting time I will never get back is that the flip control operates correctly when hosted to a reference plane but only if you use the Pick a plane option. If you select the Name option or the Pick a line… option, the flip control is disabled. It matters not at all whether you have the current work plane set to match your intent for hosting.
This is simply baffling and makes no sense. I have submitted this to Support and will let you know what I hear. My suspicion is a bug that may never get fixed, however silly and illogical it might seem.
Quick Update...
Support has confirmed my observation and has submitted the issue to development. Apparently, it behaves this way in the beta version for 2013 also. I am not holding my breath for a fix but at least I have confirmation that I an not crazy.