no thatīs not the same!
Again:
Case 1)
- Login (remote desktop connection) as user_1,
- Schedule the task at 09:00 for user_1, and logoff
- Login at 09:05 -> failed, Error=2
Case 2)
- Login (remote desktop connection) as user_1,
- Schedule the task at 09:00 for user_1, and watching what happens
-> successfull connected

The scheduled task performs a logon before executing the script, so in my point of view it shouldnīt be necessary that iīm always have an open remote connection to get this script working?!

short paragraph of http://www.windowsecurity.com/articles/Logon-Types.html:
When Windows executes a scheduled task, the Scheduled Task service first creates a new logon session for the task so that it can run under the authority of the user account specified when the task was created. When this logon attempt occurs, Windows logs it as logon type 4.

But obviously my remote connection influences positivly the functionality of this function. I canīt rebuild this behaviour on another server (independent if someone is remote logged in or not the script is working!), so i still asume itīs some specific server setting?!