I bad the same thing happen to me but when I went to the kings to find him he wasn't there.... I entered diog with the king and the only thing I could say was that Rex was dead..... Is it possible that he died... I'm not in hardcoe mode so I do t think that companions can die..... Who knows
From the Fallout http://fallout.wikia.com/wiki/Fallout:_New_Vegas_companions;
"While actively following you, permanent companions are treated as essential (unless you are playing on hardcoe Mode, see below). It is important to note that they are only essential when following you, and they can be killed both before they join you and after you tell them to leave."
So, yes, even if not playing on hardcoe the companions can die.