I'll try to answer this as a massive LOTR fan who was also dissapointed by The Hobbit movies and barely bothered to watch the latter two in theatres.
The series got stuck in an awkward no-man's land where production dragged on so long that all the initial hype about the project in the post-LOTR years evaporated and the fanbase lost interest but not long enough that a generation passed and people were nostalgic about the originals ala SW and JP and wanted to introduce that world to their kids. I myself followed the production keenly for years, wanting PJ to direct, then getting let down when Del Toro took the reins, then coming around to that idea, then there was the fiasco of whether the production would leave NZ... By about 2011 I was kind of over it frankly. The initial fans had sort of outgrown it.
There was a general sense of negativity building towards the films by release as well, people weren't impressed by the trailers and the higher frame rate look that PJ was going for and there was a lot of backlash over them splitting it into 3 at the last minute. The weak early reviews compounded this.
Lastly it should be noted that LOTR was never as big in the US as WW. ROTK was second only to Titanic WW but not even close domestically. The fandom in America was more casual and the marketing did nothing to draw back the casual audience. 300 for the first is quite a lot in retrospect, not far off FOTR numbers. Then the damage was done and the next two dropped.