Doug,
Thanks a lot, I was able to see the 'Developer' tab and I saw that "Auto-update' thing has not been selected in the document in question.
I even tried the Home Tab > Multi-level-list > Define a New...but that too wasn't working for me.
Finally I went to the first place where the bullet had disappered, inserted a bullet and set the bullet indent to be the same as that in the 'document before the bullets disappeared and then clicked on "Accept Format Changes". This change was then reflected
on all places wherein 'font style' and 'alignment' were same, but the bullets had vanished.
Thank you for sharing your knowledge, sometimes such 'shocks' are a good way to learn a thing or two :)