I only noticed this recently from watching my brother play Persona 3. When we first bought Persona 3, my brother made it about half-way through the game, before simply stopping. At the time, the main cause for the stop was the release of the final .hack//G.U. game. While we occasionally talked about restarting the game, we didn't get around to doing so until the release of Persona 3 FES gave us a strong incentive to. Yet, my brother stopped his second play-through of the game after making it slightly further than he had reached before. This time, he has switched to playing an old game, Fire Emblem: Radiant Dawn, rather than a brand new one. I don't think the timing of this is a coincidence.
There is nothing in particular about that section of Persona 3 that would have encouraged someone to lose interest in the game. As a whole, Atlus did an unusually good job of making sure that Persona 3 had a consistent amount of plot and a consistent gameplay experience. The combat in that stretch of the game was no worse than prior parts of the game. There was about as much level grinding required as in earlier levels. Heck, both times my brother stopped, he had just gone through major dramatic moments of the plot, which introduced new complications. So, a major drop-off in the quality of the product was not the cause of my brother's declining interest.
The biggest culprit is Persona 3's length. Making it only halfway through the game took over 80 hours of gameplay. Not even counting FES's newly added chapter, the game is massive. No matter how good the gameplay, a game element that was fresh and interesting at the beginning of the game is reduced to being familiar and ordinary after the player has been playing the game for a few weeks. Furthermore, the player will have probably experimented with most of the strategies and approaches that are possible in the game after enough time. The tasks that a player has to go through constantly as part of the gameplay, such as fighting random battles, leveling up characters, and exploring dungeons, gradually becomes more and more chore-like over time. In other words, the basic fun-factor of a game can diminish over time.
There are quite a few games that I have become burnt out on well before I finished them. These include Grandia, Tales of Symphonia, Legaia 2, and many others. While these games usually had a few quality hiccups around where I stopped, there was never any one thing that frustrated me into stopping. I simply got burnt out. Now then, there are a lot of factors that go into whether or not someone gets burnt out while playing a videogame, but length is certainly a major one.