Why are cells we view under a microscope dead and do not continue to divide? why do they die?
Not all of them are. It depends on the type of microscopy you're doing. If you want to look at particular cellular structures, then often the cells are permealised (their membranes are ruptured, often using acids) and the intracellular contents are fixed using certain chemicals (like formaline). Often they're stained as well so that individual organelles or components show up against the rest of the cell. All this will kill the cells.
However, there are some other microscopy techniques which don't kill the cells, and are used to look at cellular processes as they're happening.
in some of my papers at uni we look at live cells quite a lot. I find looking at cells to see which phase of division they are in is really boring but I love doing microscopy with live embyos, its fascinating. You can see them moving around all the time and in all the different phases of development (until they die which makes me sad!).
If your using an electron microscope the stuff you use to preserve and view the cells would have killed it.
