I see this life cycle:
1) Your story is new, people are popping in for the first time, they're throwing favorites and likes on there, possibly.
2) Your story isn't that new any more but you've still got your devoted fans who will read each chapter. They liked the early stuff and they're still coming back.
3) As time goes on, all kinds of things happen. The people who favorited your story favorite others and start to prioritize those. The people who favorited your story drop off the site. You yourself might take a long break (Lord knows we need that some times). Whatever the case people drop the routine of revisiting it, intentionally or otherwise.
So basically, unless you can give it a shot of hype somehow, I think its inevitable that a deep story ends up looking abandoned in those later legs.
I'm not sure of good ways to get people checking those latest chapters specifically. I think that's just going to be a function of getting more people through the door and thrilling them on. That's it's own problem, depending on things like the broadness of your story's appeal and whether it has means of exposure, like you spread it around yourself.
Maybe you could try drumming up some interest by trying out new, somewhat related stories and saying "by the way, if you like this, be sure to also check out my other story!" and providing a link? Not sure... I haven't had a lot of success getting this second wind, by any means.
Maybe try thinking of your favorite very long stories and what they do to keep you engaged? If you're like me... you may realize that, hypocritically, you can probably count the number of giant stories you actually have read all the way through on one hand.
Best of luck to you!