Anecdotally I haven't observed managers having more difficulties job hopping than engineers. In fact managers are often the first to jump the ship in stormy weather.
And once they reach the director/vp/c levels it’s even easier to do so, independent on their achievements. They always throw the classic ‘grew the team from x to y people, and from i teams to k teams’ and get an offer.
There are fewer positions, but as usual people who already reached the required level have a hard priority. So it's only harder if the total number of management positions is shrinking faster than total number of engineering positions (which might we'll be the case now though).