I have that issue and more. After this mornings listening, I tried to start where I left off. I opened iBooks and it decided that I was at the beginning of the book again, rather than in the middle.
If I let the phone auto lock, then push home and see the audio control on the screen, push pause, the time indicator goes back to the zero point of the Track. If I push play again soon, it resumes where I left off, but (and I don't know the exact time period) if I let it sit paused or leave iBooks and come back, it has lost my last listening point.
If I pause, then push play again, the time is represented in seconds/minutes since I restarted playing; not seconds/minutes into the track. This makes it difficult to figure out where I was for resuming later. If I then log back into the phone, and open iBooks, the time is not moving at all (but it is still playing).
I can use the 15 second button, but the drag feature shows me dragging out to a later time in the track, but then brings me right back to where I was.
Too many other issues to type :-(
This was great when it was part of Music.
iPhone 6s