Totally normal squabble to have even after 19 years of marriage. You two have been through ALOT together and will make it through this as well. It is sooooo healthy that you guys even discuss this and hash it out.
I have found that guys don't talk about this kind of stuff with their guy pals as often as women do with their gal pals. So guys tend to think they are alone in the struggle..and the only ones. Guys don't usually sit around skimming through questions or answering those questions on a "dadapedia" site.
Yes..my husband and I have different desires of frequency. Majority of men tend to want sex even amid emotional turmoil, stress, sadness, insecurity etc. It empowers them and makes them feel needed and desired.
During stressful or exhausting days, women tend to lean toward wanting to sleep, escape in a book or movie or sit in a quiet room with no one touching or talking to them while gulping down a desired drink of choice. Sure women want to feel desired, needed, loved and cherished but it does not have to end in sex.
There have been many a day that my husband could do the dishes for me then give me a massage, then kiss me lovingly and I would go to bed a happy and satisfied woman. But, I understand how important sexual intimacy is to our marriage so I don't often say "not tonight hun". I love our alone time together and he is very attentive so that I enjoy it just as much as he does. (c'mon...the gift of having multiple orgasms is such a huge plus to being a woman!!)
Men and women are sooo different in our chemical make up. I am soo grateful that my ob/gyn explained this to me after having our first child. She discussed sex after baby in very primitive terms. Men have an underlying innate desire to procreate the human race...women have an underlying innate desire to nurture the human race. This explains why my husband can go at any moment of the day while I usually run through the day's to-do list in my head.
You have hit a little bump whether it is mid life crisis for him or just being depressed. Having anxiety mixed with being constantly sleepy will definitely mess with his head and make him have illogical/irrational thoughts. You saying you are not that into having sex with him all the time translates to him that you are not attracted to him.
Tell him to stop saying pity sex..that is wrong. There are nights I don't feel like making dinner for my family but I do. It is not pity dinner...or pity attendance at the 100th dance recital. We do these things out of sheer love and concern for the other person's feelings. Not duty or pity...but LOVE!!
He knows deep down you adore him and love him...heck...you have stuck with each other through some of life's most tragic situations. Keep lovin' him and telling him you find him sexy. Spend time together having fun to lift his spirits.
Good luck and best wishes!!
( We are going on 19 years of marriage as well but have 3 younger kids in the home ages 15, 12 and 8. I am almost 40, my husband early 40's)