One solid reason the time-loop doesn't work and...
I have only read about 1/500th of the posts on here about the movie, so if I am posting something someone already said, please, do not freak out. Ideas concerning films aren't copyrighted, and I don't need some psycho telling me they already posted that 2 years, 6 months and 4 days ago. Anyway (my opening DID have a purpose)......
I am sure there have been many posted reasons why the time-loop "theory" or whatever you want to call it, doesn't work, but I think this is the most straight-forward and simplest explanation of why the time-loop theory does not work and why none of this is really happening in reality:
The cops following Pete are following him because of what happened in the jail cell (Fred transofmring into Pete and therefore being let out and into the custory of his parents). Therefore, these cops know about Fred killing Renee.
Towards the end these cops talk with the other cops (the cops who originally were at Fred's house because of the videotape) and establish who Renee is (We find out that it is the same person - in my original viewing, I thought it possible they could be twins. However, it being a Lynch film, my original viewing had me open to any and all possibilities knowing that I am only scratching the surface and will only begin to understand after further requisite viewings).
Then, these cops go by Fred's house and when they see Fred, they chase him. So, it can't be a time loop, because supposedly, Fred is inside the house (with Renee alive) hearing "Dick Laurant is dead," which is where the film began. Fred having to flee so quickly explains why the "original" Fred saw nobody when he looked out his window (he did take his merry old time) to see who was out there.
Anyway, I just thought that was a good simple explanation of why this is not an issue of a time-loop, but more a question of an alterate reality, or a created or imagined reality, or a purgatory-style reality (which fits in well with the existence of the Mystery Man, I think).