I'm no expert on this, so if what I say next has already been checked, then sorry.
First, since the online microphone does not record when the headphone jack is plugged in, the audio has probably already been switched. Otherwise you'd still get an audio recording, the built in mic. (Hold in mind that if you have audio sorces plugged in for both the headphone and the 30-pin port, the 30-pin port will take precidence.)
What I would check:
If possible, plug the mixer output into another recording device or audio receiver, to make sure the signal is there. Alternately, plug in a different mic/input to the iPad and see if it works. Using a set of iPhone earbuds (or other other headset with a mic) would be the easiest way to test the iPad's input.
Eliminating one or the other should help issolate the problem.
Make sure the headphone jack is a four conductor jack, and that the forth ring, closest to the base) is the mic/mixer input. It is fairly easy to mix and match 2,3, and 4 conductor jacks and end up with nothing.
I'm not familiear with the Lifestream app, but check to see if it also has input level controls, and adjust them accordingly.
You sound like you know what you are doing, so I doubt this was much help, but maybe it will jog something else loose. Good luck.