After a detailed analysis I was able to conclude the following: The scenario is to have two chrome apps - one of which is a background app, the other is a normal app but its shortcut is put in the windows Startup folder. Then we have a race condition on startup which can have two outcomes.
1. The good outcome is when the chrome process that handles background chrome apps (I assume this is the process that handles background apps. Its command line is chrome.exe --no-startup-window) starts first. This is the case when chrome puts an icon in the system tray. In this case the background handling chrome process is shown as the parent of all other chrome processes in ProcessExplorer.
2. The bad outcome is when the chrome.exe process from the app that was put in the windows Startup directory (the command line is chrome.exe --profile-directory=Default --app-id=<app-id>) starts first. In this case there is no icon in the system tray. The background app is started as it should. The Startup folder chrome app process is shown as the parent of all other chrome processes in ProcessExplorer. The problem with this situation is that when the Startup folder chrome app is closed - *all* chrome processes are killed.
This manifests on a Windows 7 machine with the latest chrome installed (42.). The same problem didn't occur in chrome 41 (on the same machine).
I used lhfiglpmnendbchimlikaeachppfonmm for the Startup folder app, and dgflkdhgdabjibkfmpefanoigejemhpc was the background app.
Thanx for the help.