I don’t have any reason to catalog books I’ve read.
@Wellspring , you must have a better memory than me. I often am asked for book recommendations but often don’t remember the exact titles or authors of books I’ve read (whether or not I liked them), so having that information recorded online is of great use to me.
I also use GoodReads. I used to use LibraryThing, and loved it. But all of my friends who catalog are on GoodReads, and I want to see what my friends are reading, and I don’t want to catalog in two places.
In recent years I’ve sometimes wished I’d cataloged my reading, since of late it isn’t unusual for me to begin a book, only to realize a few pages in that I’ve read it before.
And it would be handy to check authors’ names.
Good suggestions here, and I would add pretty much anything by Meg Wolitzer.
I’m another who uses Goodreads to keep track of books.
I’m a little surprised by those who think that there are few books out there that fit this description. 
One author that immediately came to mind was Elizabeth Berg. Several of hers will fit the bill. Here’s a link to her website where you can read a description of each book:
http://www.elizabeth-berg.net/site/epage/47234_662.htm
Olive Kitteridge is wonderful (as is the HBO mini-series starring the inimitable Frances McDormand). Another Elizabeth Strout book that you might enjoy Is My Name is Lucy Barton.
The View from Penthouse B by Elinor Lipman is a good one. Also, Tara Road by Maeve Binchy. Oh, and The Diviners by Margaret Laurence.
Ladder of Years by Anne Tyler.
The Boston Girl by Anita Diamant isn’t exactly what you’re looking for but it’s characters are an 85 year old grandmother telling her granddaughter her life story.
One of my favorite books of all time, and one with strong female characters, is The Secret Life of Bees by Sue Monk Kidd.
In the category of strong female detectives (most of them are middle-aged) there are many. Check out, Sara Paretsky’s VI Washawski series, Linda Barnes’ Carlotta Caryle series, Marcia Muller’s Sharon McCone series. One of my favorie’s is Nevada Barr’s Ann Pidgeon series. Pidgeon is a park ranger who solves mysteries at various national parks.
I read 100 books a year and keep track on Goodreads - else I would accidentally pick up stuff I had already read.
I track for the same reasons mentioned by several above. While I read quite a bit of serious non-fiction and those titles “stick” in my brain, I also like some light reading and one year I downloaded a bargain Kindle book by Emily Griffin only to realize that I already owned it in paper format. If I didn’t track, I’m sure I would do more of that from time to time.
If for some reason I can’t remember the title or author of something I’ve read it’s easy enough to check on Amazon or stopyourekillingme.com (I read a lot of mysteries.) I’ve never had the experience of starting to read something and realizing I’ve read it before except maybe once or twice when a book was reissued with a different title.
I think there’s room in life for people who record their reading and people who don’t.
@Midwest67 Call me a curmudgeon, but I refuse to track my reading in Goodreads (or own a Kindle). I think Amazon is detrimental to the publishing industry (owns Goodreads), and I refuse to give them access to my books read or TBR list. I read a lot on an inexpensive Samsung tablet with a Wi-fi only connection.
My D1 and I both use an app on our iPhones called Bookcrawler. It is the most important thing on my phone to me. I’d rather lose my contact list (or my CC access 
) than my reading list.
I understand the Amazon concerns. I track on Goodreads but don’t own a Kindle and, when editing book reviews, always try to include the actual publisher as the purchasing source instead of Amazon.
It’s too late for me! I’m an audiobook girl. I use Audible, and = Amazon.
I’d like to start keeping track. I’m terrible about remembering titles & authors.
I don’t keep track, but occasionally I need to double check whether I’ve read something or not. (Many of the books I “read” in the car are light reading and not memorable.)
Jeanne M Dams has a series about a middle aged/older woman who solves mysteries.
MC Beaton’s Agatha Raisin mysteries feature a middle aged private investigator.
Another vote for the Mrs Pollifax books.
Elegance of the Hedgehog was lovely.
Alexander McCall Smith is a wonderful writer and his Isabel Dalhousie books feature a main character who is younger middle aged. The Number One Ladies Detective Agency also has a strong female character who is a bit younger.
There are older female characters in some other books, like some of the newer Tom Clancy spinoffs, where the head of the CIA is an older woman.
Elly Griffiths’ Ruth Galloway mysteries are good, too.
I started logging my books when I was trying to recall a book I loved but could not remember the title or the author.r. However I remembered very specific things about the plot so asked my librarian. She used some of the key words to look it up in LibraryThing, a cataloguing system popular at the time among librarians. I used LibraryThing for a while but then at some point switched to Goodreads years ago. I do not own a kindle - I mostly read library books. I do have the kindle app but use it to read ebooks checked out thru my library. Not only do I log the books I read, but I also have shelves (tags) so that they can easily find books I read but don’t necessarily remember the title (for instance, some shelves are by genre such as historical fiction, memoir, mystery while other shelves would be setting such as Asia, Africa, southern US, and then also subject matter such as dysfunctional family, racial tensions, dogs). My friends and I recommend a lot of books to each other. By having the books I’ve read catalogued this way, in addition to a rating and what I liked or disliked about a book, makes it easier to suggest books to my friends. I read 60-70 books a year so this makes it easier for me to keep track.
Getting back to the original question, too bad I don’t have a shelf for “middle-aged female character” b/c then I could easily find some suggestions. Tbh, I imagine a lot of books I read have middle aged female characters but it’s not something I’ve given much thought to. Many books I read seem to take place over a long period of time where at some point the main character is middle-aged.
I’ve never kept an online list of the books I’ve read. Yet, as leader of one of the city book clubs, I’m often asked for a list of good reads. I keep a list on computer, and reprint it for,people. What would You Suggest? Bookcrawler, as Inparent mentioned, or Goodreads?
In This House of Brede by Rumer Godden: many middle-aged women, almost all of them nuns, in this one
The Franchise Affair, by Josephine Tey: a mystery, with a mother and middle-aged daughter accused of a crime. Her better-known book Brat Farrar also has a middle-aged woman as a major character.
https://ebooks.adelaide.edu.au/t/tey/josephine/franchise_affair/
Consider This, Señora and Stones for Ibarra by Harriet Doerr (whose 1st novel was published when she was 74)
And To The Lighthouse by Virginia Woolf. Mrs Ramsay, the female protagonist, has at least 6 children, several of them grown up; she’s based on Woolf’s own mother.