"Keep Together" applies at a number of levels and I suspect that's what's causing your issue. Try this:
1. Right-click on each subreport, format, and turn off "Keep Together".
2. Also turn off "Keep Together" on all sections within each subreport.
3. Put the subreports in separate sections.
4. In the Section Expert, turn off "Keep Together" for each of these sections.
-Dell