Is there anything to be done about being blacklisted at work?

I work for a large company. Everyone agrees that my work is creative and good. Recently when I came up for a big promotion, I didn’t get it. Only later did I come to learn that it was not due to competence but rather to a possible personality conflict with a more senior person (or multiple people). A major problem is that I don’t really know who has the vendetta, and why. In any event, I’ve now essentially been strongly encouraged to move on, which would likely mean moving to another city. However, I’d like to stay, since I like the area.

So, my questions are:

1. Is there anything I can do? 

2. Should I try to speak with the senior people in a frank manner and try to understand the issue(s)?

3. Is there a way to repair the relationship(s)? 

4. Should I just cut my losses and start over somewhere new with a clean slate?