No. I don't believe gentlemen are a dying breed.
With sexual equality the rules have changed.
Chivalry for the most part was born out sexist attitudes.
Gender rules have changed so much that (the safe thing for most men is to treat women exactly as they would other men.) Compliments/flirting can be construed as "sexual harrasement. "The Romantic Chase" today is called stalking.
"Oftentimes when a man opens a door for women there are just as many who will NOT say, "thank you" as there are who will.
Some in fact resent being "forced" to acknowlege an act of kindness from a strange man and they would rather open their own doors.
If a man happens to say, "You're welcome!" The woman is very likely to say, "I didn't ask you to open the door for me!" Once again instead of men trying to (guess) which women would welcome a gentleman and which would be offended, he chooses to just treat them like "equals".
Personally speaking if I'm walking through a door and I sense someone is right behind me whether it be a woman or a man I'll reach back to keep the door open.
The behavior of (modern men) has changed in response to the behavior of (modern women). It's a difficult balance to strike when someone wants to be treated as an "equal" and "special".
We live in times where most people are only friendly or kind to someone of the opposite sex when they are "interested" in them.
Some women automatically believe an unknown man is hitting on them if he smiles and greets them with a friendly "Hello", or "Good Morning". If the woman is NOT interested in him she will give him a look that could kill!
It's a sign of the times! LOL!