Have you checked for objects that are text-wrapping, perhaps unnecessarily?
Have you looked closely at the text to see if it has doubled returns between paragraphs?
Have you checked to see if other subheading styles near the text are set to a Keep With x number of lines afterwards?
You also need to check the options for predeeding and following paragraphs and waht is set te keep with previous or keep with next. It's usally a problem that you've got a paagraph set to keep withthe one that's breaking, and that one is set to keep too many lines together to fit the space.
Also uncheck Keep with Pervious, and Keep with Next set to "0"
Thanks for the answers, I checked everything that you suggested, but nothing worked. So I removed every paragraph style from the text, which I have problems with, then redefined them, and the problem got solved. Maybe the problem was that the base of the original styles were imported from ms word..