"I always have the feeling that Im losing something," she said
But still, her words moved me.

These are two of the first few lines of the movie, and he IS referring to her, isnt he? If that person is dead, the wording would be different, like "she used to say", or the like. That would have indicated her death, even if it is just slightly.

And you seem to have missed the idea of an open ending. No matter how open it is, it is still an ENDING, meaning the end should be based on the story and the events that happened there. If you assert that you can just freely decide on an ending just because there is a huge time gap, then there is no point watching the movie at all. And in truth, the ending isnt as open as you say, since it did have a solid ending, which was positive however you look at it.

But, it is your freedom to think what you want. It really is none of my business whether you think Sayuri died or not, but I just thought that the greatness of this movie is being wasted if it is appreciated on such a level, no offense. The ominous intro paired with the happy ending is one of my favorite parts of the movie, I just didnt want it seen so wrongly.

Ryllharu - Agreed with the positive ending part. Though I said the split up ending is possible, it is unlikely, at least compared to him just reminiscing alone in order to set the general mood of the story, and setup the surprising ending.