One way that has been done before is that Inuyasha meets someone else in the time they are apart and is mated when Kagome comes back...you could try that.

Hey if anyone has read my first fanfiction "A Door Already Open" you would know I'm trying to shift the story from Inu/Kag Sess/Hema and switch over to Kag/Sess. I am currently stuck on how to go about doing that. I kinda want to kill of Inuyasha in a realistic way, but I wonder if its also possible to shift to them without killing any of the main characters off. I would love some feedback or ideas on how to go about the next few chapters on switching to Sess/Kag. Please help if you are able.

I haven't read your story so I don't know about the time line, but one realistic option would be simply drifting apart. People change over time and so can their feelings. Kagome and Inuyasha especially being so young in the canon, I could easily just see them growing up in different directions.

Also sometimes, no matter how much you care for the other person, and even if the feelings were mutual, you're just not a good match for each other. Lack of communication to my understanding is one of the biggest underlying reasons in relationship problems.

Especially for Sess, external factors could also be weighing in, like stress from work/ruling the lands, or perhaps disapproval of his relationship from his peers/subjects, plenty of things like these could start putting strain on him. He could become more short-tempered or maybe withdrawn and that in turn would put strain on the relationship until it simply could not take it anymore.