[Renate]

That's strange. I don't use KOReader, so I can't address it exactly.

Conceptually, there are two parts here which may to a lesser or greater extent be separate or merged.

The first part is the library that knows what books there are and when they were last read.

The second part is the reader that can display books.
It takes Intents (basically commands) like "open Jane Eyre" and does it.
Without a specific command it can ask the library what was the last page it was reading and go there.
The reader doesn't update anything when you turn a page (unless you use a Kindle and it's keeping track of EVERYTHING).
When you switch to another app or sleep it updates the database.

Can you see a list of your books and it's sorted by "Last read"?
Does it seem to track correctly?
Is there some option in KO reader that you don't have turned on?

I use my own library/reader and there are two icons, one for Library, one for Last read.
If I'm bouncing between books, I just need to go to Library (sorted by Last read) and click the second or third.