Two things kicked me into thinking about this subject. One, I wondered why I couldn't get involved in this or that series when as a rule I like revisiting characters, and I might like the elements of a given story. I bombed out of Anne McCaffrey's Pern stories because after the first few, I kept feeling I'd already read the stories. Ditto with Darkover, though for slightly different reasons.
Many series deposit the characters right back at the start, a la television series.
You knew at the the end of a Trek story that Kirk would never resign, or get married, that Spock would always be the science officer, etc. In others, the problem is more difficult to define. I sometimes wonder if the writers of series that I am fond of, and return to again and again, discovered their overarcing theme as time passed in their own lives. At some point along the way, the threads didn't just braid, but melded together into a whole. Writing This in turn causes me to wonder if the experiences of our own lives, and our cumulative insights, can at last help us to see our big themes.