It turns out that when you try to test simultaneously two (or more) AIR applications, in the moment you try to open a second one, the first one is killed.
That wasn't typical behavior in older versions of Flash. It also isn't how Flash Builder is working.
It was extremely difficult for me to debug this one. It involved running BSD features like Accounting and Auditing.
What I have found is that Flash CC actually calls "killall -9 adl" command before it runs an AIR application.
It is happening in "/Applications/Adobe Flash CC 2015/Adobe Flash CC 2015.app/Contents/Common/Configuration/External Libraries/FLAirDesktopExt.bundle/Contents/MacOS/FLAirDesktopExt"
It looks that this will also be true for Air Android apps, but I haven't tested it.
I need two instances to run to test SERVER <-> CLIENT applications.
What I have finally done is to hack the file in a hex editor and replaced "killall" with "killapp" (just a dummy comand that does nothing (hopefully).
That did the trick, so I can now work on my apps.
What I wonder is - is this killall command necessary at all, especially as it wasn't the behavior in older versions nor in Flash Builder.
This post is also intended to help anyone who stumbles upon this issue, as I wasn't able to find any solution online.