I would add that it is important to also consider Emily's status as metaphor for the post-Civil War South -- antiquated, decaying, unable to progress or move forward because she is hampered by too many memories. The watch (stopped progress) echoes this. It's a particularly specific statement to make when addressing the issue of a Southern woman who is a member of the fallen aristocracy.
I think that it's representative of Miss Emily's incredible will: she insists on the world as *she* understands it and if that means stopping time, so be it. I don't think there's any textual evidence to suggest that it stopped with her father. It seems more likely to me that it stopped (or that she stopped it) with the murder of her lover. Like so many female characters in the Southern Gothic tradition, her insistence on living in a world as she would have it - as opposed to how it is - is a full flight from reality. But what is interesting about Emily (or Blanche in "Streetcar" or Julian's mother in "Everything That Rises Must Converge") is the way the people around them aid and abet that flight.
Miss Emily is a relic. A representative of a time period and an era long gone. This is represented by the once-regal house being surrounded by gas stations and other "modern" items that have encroached on the territory of the old aristocracy.
The watch...stopped...represents that her life is no longer what it once was. With the death of her father, her life, in a sense, also stopped. She lived in the past up until her death. How appropriate that the watch should be stopped to show the reader that she is unable to move on into the future?