Thanks for the screenshots...that is really weird. I don't believe it's the margins in the text frame itself that's changing...all that would do would be to cut off more of the rows. What's happening is that, for some unknown reason, your cells are actually changing size. Whenever strange things like this don't make sense, I repair permissions. For instance, my Tabs palette is often blank unless I repair permissions. It looks like you're on a Mac, yes? If so, quit InDesign, repair permissions and see if you have any better luck.
One thing to check is the Cell Options settings (on the table as it sits on the pasteboard where you have it looking like you want). Check your Keep Options and set them to Start Row: Anywhere and check Keep with Next Row. That might help. A workaround would be to select each row and set the height to be "Exactly" whatever its measurement is (that should prevent the resizing of the cell)...and/or set a maximum. Time consuming, but it might be the workaround.
If all else fails, you might have a corrupt file...does this happen in any other file? Can you copy and paste into another document and still get this problem?
Okay...that's a lot to work on...maybe something will help.