Couldn't this mean that she just couldn't/didn't die until after Aragorn died?
That is exactly how I read it - it was not the Gift of Men (death) that she gained, but the love life of a mortal man, Aragorn. She was not fated to die until she lost him. And how can she "lose" the Gift of Death, when Tolkien clearly says in the 2nd to last paragraph:
"There at last when the mallorn-leaves were falling, but spring had not yet come, she laid herself to rest upon Cerin Amroth; and there is her green grave, until the world is changed...."
I don't know about everyone, but this says to me that she died a natural death, esp. "laid herself to rest", "green grave". She did die a natural, human death.