I've finally found the solution. It was indeed a "ie-compatibility" issue, yet not obvious and not that easy to find.
Probably some wordpress plugin added the following line to the header:
<meta http-equiv="X-UA-Compatible" content="IE=7"/>
I changed it to
<meta http-equiv="X-UA-Compatible" content="IE=8"/>
And it worked. Why do I say it was not easy to find? Well, I played a lot with compatibility settings in the IE browser and nothing worked. And again the way the bug represented itself would never make me think that such line was responsible.