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Some really good answers here! For me it's mostly a mix of what @Rahul-Balaggan and @Jon-Mitchell detailed out... either I want or need to re-experience a specific story that I crave or doing so reminds me of a time and place, when I first read the story.
For me, doing so triggers a kind of nostalgia for the emotional experience of having read a particular story. For example, when I was in 4th grade my mother sat down with her copy of the Lord of the Rings that she had probably since highschool and read some to me every night. Then, the following summer, I took the same books and read them to her instead. They sit in my bookcase now, having lost her a year and change ago, and simply looking at them triggers a wave of different emotions, to say nothing of reading them.
I don't actually re-read that much though. What does happen pretty often is I'll remember a particular phase or event in a book and I'll pick it up, flip right to it - I've never used bookmarks, never needed them... even as a kid I had an natural ability to pick up a book and flip right back to any part I'd read - and I'll re-read that specific part again. And usually a bit after it as well, of course. Though that really only applies to physical books.
I don't know that I can point to any LN's that I've re-read a bunch though. Not because I wouldn't or that they don't deserve it, I think it's more to do with how much new there always is to read. And if I'm honest, I think a large part is also just in how I consume LN's. I am not a digital person, I only have a handful of books in my Kindle account and most of them are cookbooks. I love the convenience of digital, intellectually, but I'm a pure bibliophile... give me printed paper that I can hold and pages to turn, where the decision of where to read can have as much meaning as what to read, and that's where I build those emotional connections. I wouldn't be able to read as much if we didn't have digital, but the cost, for me at least, is that I don't build the same depth as a result.
