Yes, Plotties can die. Natural causes, negligence or disease can kill a Plottie. Of course, injuries or accidents can also be fatal to a Plottie if they are serious enough.
Plotties can be affected by a large number of diseases, most of them being caused by fungi, bacteria or insects. The most common symptoms are loss of vitality, spots, rotting parts, swollen patches, drastic changes in color or scabs. Most bacterial or fungal diseases can be treated with special pesticides, preferably organic ones.
Big changes in temperature can also cause your Plottie to get sick or even die. Cold and Heat strokes and dehydration could be some of the results of such sudden changes.