Short answer, yes, coral can die. Just put it in my tank.
Seriously though, it depends.
Corals are nothing more than tissue, like a plant, so theoretically, they can live indefinitely, like plants. Plants usually don't die unless something kills them.
In the case of a coral, each polyp is a completely separate organism. If you look a a frogspawn with 25 heads, one might think of the death of the organism to be the complete death of the entire "coral," but this is actually 25 different individual organisms dying.
While a polyp may be able to die due to natural (and totally non-external) causes (and it may or may not be able to, I don't know), usually, new heads grow faster than heads would die, so the coral in the sense of how we look at them can live on forever by simply multiplying.
Of course, this logic does no apply to an LPS, such as a Tounge, plate, or Bubble coral, in which case the loss of one polyp is what we'd interpret as the loss of an entire coral.
Again though, death is almost always (if not ALWAYS) caused by external conditions.