I think we need to divide this topic a bit into two questions:
1. Why are people not replaying games with new save files/playthroughs more often?
2. And why are people not continuously playing already completed games more in multiplayer/on the same save file?
Because both probably have different answers.
For number 1, I'd say game length and linearity has a lot to do with it. Many more 'modern' games take about 40 or so hours to complete, so plying a new save file means more going through endless sidequests, more playing the parts you didn't enjoy as much the first time, etc. They're also a bit more linear, which often means that replaying a triple A game is kind of like rewatching an especially long film rather than playing a game. Contrast to older games (which despite difficulty could be beaten in under an hour or so if you knew how) and I suspect on some level, games have just lost much of the replayability due to becoming more like overly long movies.
The second one might be due to the internet and AHDD. Seems like gamer attention spans have dropped significantly, so the majority seem to lose interest in things after a month or so like a somewhat hyperactive, spoilt five yar old. Add gaming sites that cater to this (because hey, most gaming site traffic is based on hype and 'timing' more than quality) and I suspect a lot of games just drop off the radar once the very 'casual' audiences move on and the gaming sites seemingly drop all coverage.
And maybe people being a bit more spoilt when it comes to new games had an effect. I mean, back in the olden days, there was definitely a feeling of games being something you got fairly rarely, likely maybe every few months or years or so. Hence people wanted to stretch out every last drop of value from them, playing them long past the point others might have moved on. Now though, I suspect the ease in which games can be bought cheaply (thank you internet, app store, steam, eshop, digital distribution in general...) and a generation shift (perhaps todays parents being gamers themselves has something to do with this) has meant that people tend to get new games a lot more regularly, especially the kids. Which might explain why so many games drop off in popularity in about a month or so, because the majority 'kids/teens' audience seems to get new games at that rate now.
The only games that take over 40 hours now are some RPGs and they did that even on days of the NES - especially games made by Squaresoft and Enix before they partnered.
for topic number 1, I think DYL sums it up the best in another thread when he said how lack of a save state adds replay value, like in Mario one where if you stopped or died you had to try from the beginning all over again. It made the game more fun and challenging.
As for topic 2, I can't stress how much more fun a game is with a second player who is not a total moron. whether it be AI-controlled or a real person behind a controller, if the second player is inept then the game is severely less fun and more aggravating. For example, I've played Saints Row 3 by myself fully 3 times and with several friends fully numerous times. I enjoy seeing their reactions to the dialogue and scenes as much as when I watch a movie with someone in real life.
As for the same save file aspect, I have no clue. that one is new to me. I never noticed it.