I think demand will be high for the next 5-7 years and then will wane.
Like most things in life, this is about supply and demand. Demand is set by $ so as companies like Google, Apple, Amazon, Facebook, etc. continue to grow year after year, the demand for software engineers will continue to grow. It's also not only large companies because as the big companies do well, they acquire small companies so startups flourish which means VCs flourish, etc. Growth is still strong in tech companies although some will say that they aren't growing as fast as they were before.
On the supply side, there are more and more students going into college with the aspiration become a software engineer. Remember the 80s when everyone wanted to go to med school? Well, now everyone wants to be an engineer. There are thousands of schools around the world that are teaching Computer Science to graduate the next set of engineers. There are thousands of students graduating every year ready to take on the demand.
I say 5-7 years because with the demand high but rising at a slower rate than before and the number of CS grads increasing year after year, it will hit an equilibrium.
I went to college in 1991 when there was a recession and most of my fellow CS classmates felt that there would be work but not much work when we graduate. The word on the street was that companies laid off people and found a way to work with less people so even if the economy gets better, they still wouldn't hire us. I studied CS because I liked it and was good at it.
However, I will be bold and venture to say that there is no shortage of engineers today. I spent the last 10 years actively hiring for the companies where I worked and for every software engineer opening, I got hundreds of resumes. There's no shortage of engineers. However, not all of them can get jobs because there is a shortage of good engineers. Anyone can read a book or take a few classes and send a resume saying that he/she is now a software engineer but it takes a lot of work, intellect, and experience to become a great software engineer. Heck, some people have told me that many interview candidates can't even code fizz-buzz and when I ask a simple binary search question, most of my interview candidates get it really wrong. That's just the basic stuff. Great software engineers will always be in high demand.