Marketa,
I discovered what is causing this behavior - checking the Open in Browser option. When I unchecked it everything worked as you said.
The only thing I can think of that would cause this behavior then is that the previously exported file (which you're probably already viewing in your browser) is busy and can't be replaced, so the OS is presenting this dialog, or perhaps the browser is presenting this dialog to you. Try leaving the checkbox turned on, but close the window in your browser that you're using to view the exported images before you start any further exports.
-Kirk
