I don't think the demise of Enterprise is solely on the shoulders of fans. Of course it's not. the franchise in it's current incarnation had played out. There was and still is nothing more to do. But it seems to me, the constant campaigning against the show by some hardcore fans certainly didn't help.
I don't think the "constant complaining" of the fans made any more difference that similar "constant complaining" about any other aspect of the Franchise does. "Enterprise" held on to almost all of that little core of devoted trekkies - a few million, in the U.S. - throughout its run. At least nine out of ten of the folks who complained on Internet boards about the show watched it pretty faithfully. It was the show's inability to attract or hold anyone other
than trekkies that doomed it.