There were a number of separate disasters that took out the old boardwalk in the early 60s. Both the two anchors - the roller coaster block and the old pier (the one discussed here, between 3rd and 2nd Ave. N) were already gone by the time Dora rolled around in 1964.
The need to do something had been noted since at least the late 50s, but the Jax Beach city leadership was unable to come up with anything. People there at the time remember that the coaster block (then containing the "Wild Mouse" coaster) had become downright unsafe, with flammable materials being stored in dilapidated, poorly wired buildings right next to the attractions. While the owners and city were debating what to do, nearly the entire block was destroyed by fire on March 9, 1961, taking out the "Wild Mouse" and most of the associated attractions. The city then spent several years fighting over the property with the operator, W.H. Adams, Jr.
At the same time, the city took ownership of Shad Pier in May 1962. It had been an attraction unto itself in its prime, but outdoor dancing pavilions were seen as old fashioned and the pier was in as bad of shape as the coaster block. While the city deliberated what to do with the pier, it too burned down on October 13, 1962. A private investor, R.L. Williams, built a new pier at 6th Ave. South, several blocks outside the tourist zone. It was built specifically for fishing and had no dancing pavilion. This pier was damaged by Dora in 1964, but was repaired. This was the pier that was severely damaged by Hurricane Floyd in 1999. In 2005 it was replaced by the modern pier at 4th Ave. North, closer to the old pier's location.
Dora took out or damaged even more of the boardwalk, and none of it was ever rebuilt. Times had changed and those kinds of attractions were seen as passe, especially as Disney World and its ilk were already in the works. Tourists were less and less interested in small town attractions. Additionally, the development of A1A, Beach Boulevard, and Atlantic Boulevard effectively turned the roads into strip mall-lined arterials that reduced the need for a central commercial district and spread the population west and south. At the same time, the Beaches area was increasingly becoming a bedroom suburb of Jacksonville, and the easy access to shopping and attractions took away much of the appeal of the old commercial and tourist district, which was seen as increasingly seedy.
By the time I was growing up in the 80s and 90s, the downtown area of Jax Beach was generally seen as a place to be avoided. The city made things worse by doing nothing or worse. Large portions of the area were leveled in the hopes that some big developer would come in and build something new, and the few new amenities that were added were pretty lackluster (case in point, the Flag Pavilion).
In the 1990s the city took a new approach to redevelopment by encouraging infill and working with local business on development strategies. From that point there has been a much more comprehensive master plan, and it has clearly paid off. There's still more to be done, but the downtown area has become a nightlife center for the whole metro area.