At all the companies I have worked at till now (MS/Amazon and Snap) - we always have a hard-time finding good experienced engineers. So I would contend the reverse: It is actually awesome after 35-40. By this age group - I think many engineers have moved on to careers in management etc., So the ones who remain are in high demand.
There are a few big catches though:
- You better be really good in both development AND engineering.
- You better be able to work with people. You may not be a manager by now, but mentoring takes on a giant role few years in. And very few opportunities arise where it requires a single heroic effort (capitalize when it does happen).
- As @tptacek covered elsewhere, you better have one field you are really good at.
- You better be very good at picking up 'new' stuff and identifying similarities to what you have done already: most of the learnings carry over, you eventually figure most of it is pretty much the same ketchup in a different bottle. BUT there are usually some incremental advances: your ability to catch on to these matters a lot.
- Companies have always liked the 'T' candidates: Who can operate in a broad set of areas and have real deep knowledge in one field.
I don't know how to say the following without sounding proud, but I think it adds relevant data points - so I will just put it up here: In my case (15 years?) I have done a ton of server development, I am trying to do some actual client(ios/android) work in addition to generic consulting. But my depth is around data - I have worked on multiple storage engines by now, built a bunch of database systems. I have never really sold my resume based on languages or technologies (they come and go - I would estimate I have worked on anywhere between 20-40 languages based on how loosely we define that, most experience has been with c/java/python). Last time I was looking to switch jobs 2 years ago, I had offers from almost all the big companies in cs within a month.
Sadly I don't have data points on how easy it is to enter this field beyond 35 :(.