Ok. I've found what it was.
a) The problem is internal WebException in XMLTextReaderImpl. This WebException says "Server unavailable. Error code 503".
b) The problem is reproducible also with mageui.exe. The problem happens when I select New application manifest, select the folder with the client and click Populate => mageui.exe shows me shortly after that a standard Windows error message box with options Debug and Close.
c) The cause of the problem are our license files (for instance, log4net.htm) which are also located in the client folder (we must of course deliver our software with appropriate licenses). File log4net.htm references internally to several other URL addresses which seem to be not always available. And obviously mage tries to connect to them. If I delete the licenses, then everything works properly.
Now the question: Why the heck is mage trying to access these addresses?