I think the problem the straight mystery genre has with developing
characters throughout a series...is well the same problems that television
"episodic" dramas do with it, it can detract from acquiring new readers.
Many readers want to dip in occasionally, without having to read the whole
series. Agatha Christie and Conan Doyle in a way set that up. Focusing more
on the "mystery" than the characters. And the guy who set up the mystery
genre or created it, Edgar Allen Poe, focused more on plot less on
You can't have the principle characters change too much...or it loses some
of what attracts that readership. That said, some have. Patricia Cornwell
developed her coroner and characters over time, until she hit a wall and it
felt...okay gone on too long. That's my other difficulty with the mystery
series...is they go on too long.
Five - Seven books is okay, but once the writer goes past the seven mark,
for some reason or other, they start to phone it in and repeat
themselves...the writer often has grown tired of the characters and is just
going through the motions.
Historical/fantasy series work better, because often the writer has a
definitive arc in mind. Such as GRR Martin's Song of Ice and Fire series,
(although even he ran into problems and ended up writing himself into a
corner...in books 4 and 5. But that's set up as a 7 book series.) And JRR
Tolkien. Epics work better.
But the mystery of the week series...with just one or two characters...are
going to get stale for the writer by book 7.