For all those, who have this problem, I found out the solution for the V4.1.15-8-default:

1st: keep cool (it took me several coffees to calm down on this silly thing. If the value for timeout is 0, so the setting is off or the value is wrong. Why the heck, wasn't this catched by the program??)

2nd: Login on your webserver, go into the i-doit-folder in the apache-webfiles (f.e. SuSE: /srv/www/htdocs/i-doit/…)
3rd: find the globals.inc.php
4th: open it with your favourite text-editor
5th: find and copy the following line:

$g_config["sess_time"]  = isys_settings::get('session.time', 300);

6th: uncomment one of the original one with two slashes

// $g_config["sess_time"]  = isys_settings::get('session.time', 300);

7th: change the copied line:

FROM

$g_config["sess_time"]  = isys_settings::get('session.time', 300);

TO

$g_config["sess_time"]  = 900;

8th: SAVE the file, but leave it open in your text-editor

9th: Login to i-doit and change the value for Session Timeout in the Settings. 3600 (1 hour) might be a good value. Save the sessings

10th: uncomment in the globals.inc.php

// $g_config["sess_time"]  = isys_settings::get('session.time', 300);

and comment the line

$g_config["sess_time"]  = 900;

That's it.