The sad fact about replaying VNs... is that VNs don't have replay value.
That's not to say it isn't possible to replay a VN and enjoy it. With many of the more complex VNs, it is impossible to take in the entire thing on your first playthrough, so it is usually worth a second one. Others are so well-written or have such great characters that they are worth reading again and again. Yet others are just so much fun or are so funny (games made by Rosebleu, Lamunation, etc) that they are worth playing again and again. Last of all, there are those that are so unique that no other experience quite equals them.
However, even amongst the best VNs, there are ones I've found that pale immensely after the second playthrough. In particular, games that are heavy on mysteries and rely on their hidden aspects for at least some of their attraction become much weaker on later playthroughs.
As an example, one of my favorite VNs of all time is Hapymaher (VN of the Year 2013). This game has an emotional, psychedelic story, a unique style, and the single best VN soundtrack out there. However, whenever I attempt a third playthrough, my knowledge of certain aspects that come to light in the end and the fandisc ruins it for me. Oh, Keiko is still unreasonably sexy for a chippai character, Yayoi is still funny, and Saki's sadism+jealousy thing with the protagonist is still just as hilarious... but I always stumble at two-thirds of the way through the common route (otherwise known as the 'Week towards Christmas' chapter by some fanboys). This part is immensely funny and interesting the first time you play it through... but without being able to share in the mystery and surprise of the characters, it is unbearably dull, sadly. Every single time I go back into this game, I stop here.
Another example would be charage, in general. Understand, as you know, I am not terribly fond of charage in and of themselves. I won't go so far as to say I hate them, because I don't. However, if it is the choice between a nakige, an utsuge, a chuunige, and a charage... I'll always pick the charage last. In a good charage, the slice of life and character interactions and development are the best parts of the game... but when it comes to replaying a VN, this tripod of specialties is a poor substitute for an interesting story. I have managed to enjoy replaying a few charage... but most I drop after one path (usually the one of the heroine I liked the most), simply because I feel fatigue from having to slog through the same slice of life scenes a second time.
The Light at the end of the Tunnel
However, there are some games that survive multiple replays well. Nakige, utsuge, and games that go for the emotions in general are the most obvious genres (that are mainstream). I can still go back to moldy-oldies like Haruka ni Aogi, Uruwashi no for a good cry, and I can still devour games like Houkago no Futekikakusha without any trouble at all.
Another type that survives well are well-designed comedic games... for example, Lamunation, with its endless humor (ranging from sex jokes to penguins enjoying Mexican beer), endures multiple playthroughs quite nicely, without paling much as long as you space them out. Comedy is comedy, and as long as you don't overdo it, it is possible to enjoy a good comedy VN multiple times without much fear of boredom.
Games that have a strong protagonist. Perhaps the biggest reason many Japanese VNs are almost unreplayable is because of the 'average protagonist'. A strong, well-developed protagonist with his own unique flaws and personality can carry a game on his back through numerous playthroughs. Good examples of this are Asagiri Kaito from the Akagoei series, Shirasagi Hime from the Tiny Dungeon series, and Narita Shinri from Hello, Lady.
Games that have an overwhelmingly unique cast of characters or setting. A unique setting or a cast of characters can be the difference between a boring failed attempt at a second playthrough and four or five enjoyable playthroughs. Some examples of these are Evolimit; Devils Devel Concept; and the Silverio series. (note: Chuunige are the most likely to fit this type, but the Majikoi games and the Shin Koihime series also fit into this).
In the end though, taste matters. If you didn't enjoy the VN the first time, you won't enjoy it a second time (with rare exceptions). If you don't like chuunige, you most likely won't enjoy DDC or Silverio no matter how many times you attempt to play them, and if you don't like horrible things to happen to your characters, you will never enjoy Houkago no Futekikakusha. I've known people who enjoyed all these games on a first playthrough, were able to enjoy a charage on a second playthrough, but couldn't enjoy these on a second one. So, while this is my analysis, it is not absolute, lol.