Why did he never make an appearance in which he was clean shaven from the early 1980s and onward?

I guess he just liked having that facial hair. In the Untouchables though he only had a mustache. That's the closest to clean shaven he ever got in that era.

Sometimes actors and actresses who made their mark as sex idols dramatically change their look in middle age to keep people from begging comparison to what they used to look like when they were at their peak. It worked in Connery's case because when he went bald and grew a beard, people stopped caring about what he looked like as Bond in the 1960s.

Others do it because maybe they grew up admiring a middle aged personality and decided to look like him when they reach that age. For example, there's no question that David Letterman grew a beard because he admires historic figures like Walt Whitman. Maybe in Connery's case, there was an older actor he admired when he was younger and decided to emulate when he got to be that age.