Please try to clean browser cache/cookies etc and try to reproduce the error.
Or use a different browser after moving of groups become impossible.

I had this problem too and I think there might is a small bug.
As a workaround a clean cache IMHO will do the trick.

Would be nice if you could try that and tell us if the problem vanished.

Please also test if you can reproduce the problem with other browser (FF3, IE8). Firefox 2 is really outdated.

Did you export that survey in a state where groups were stuck?
If yes, that great. Which group is it?

To jelo: i tried CCleaner before, then FF's built-in cache clearing, but did not helped. I switched to IE8, but the error could be reproduced. However, i have no access to the server / limesurvey install directories to clear the caches there - if cache clearing is possible there.
I also tried to access the admin area from another PC (and other access network), but with the same result. Please see attched two files, it even stucked on the small survey also after 5-6 reordering attempt. It can also be seen, that the group order is different in the list as it is in the dropdown list next to it (this not bothers me much), but during a survey tryout, it even displayed the groups in a different, 3rd order: Welcome Msg - U - ERTEKELES... - ERTEKELO... - Y - ... Maybe the accents could be the problem?

To Mazi: I tested it with FF8 also - unfortunatelly with the same result. I'm aware, that FF 2.0 is outdated and would use FF 3.5 happily, but can't do that because of Typo3 4.1 (rteHtmlArea probem with FF3.X).

To c_schmitz: Dear developer, i've just started using LimeSurvey a few weeks ago, but since i enjoy working with it much and appreciate your efforts to make it an even better product. Back to your question: YES, i exported as it was in a stucked state; but i also noticed recently, that if i export a stucked survey, then import it again, it become good and can be reordered again without problems - until 5-8 another reordering step. Therefore please test it by reordering various question groups more times: to the front then back to anther position, then another group to the front etc. It should stuck after less than 10 moves as i noticed. At first only one group stucked (i don't remember which one) but 4-5 more moves after, and ALL groups stucked in their position! Really crazy and also annoying a bit... I really hope, that someone could find the real root of this problem and even some solution to it.

Attached two fixed files. The issue became only apparent after trying the 2nd last question to move after the last question. At that point the first questions got stuck. This affected groups and questions.

The patch does not fix existing stuck problems. These should be fixed after deleting or adding a new question/group.