What happens when a case is dismissed because the plaintiff does not show up?

That depends on the circumstances.

Added: But it is always something that should be requested if they do not appear. The court will make a determination of the circumstances of the officers FTA. Oftentimes the very nature of an officers work requires that he be involved in, or tied-up with, another case and he simply cannot make it. However, if it is determined that, through negligence, they FTA'd the judge may dismiss the charge for "want of prosecution."