The phrase "perpetually impressed" is correct and can be used in written English.
It means constantly or consistently impressed. Example: She was perpetually impressed by his intelligence and charm.
Scott, one of my other bandmates, seemed perpetually impressed with his own disobedience, which frequently landed him in trouble for smoking, spitting, swearing, and other habits that matched his patch-covered motorcycle jacket he sincerely gave no fucks about the rules, and I thought that was pretty awesome.
I am always impressed by the frisson in my class when students realize that there's a sense in which Sartre is right: they could, right now, get up, leave the classroom, drop out of school, and go live as beach bums in a perpetually warm climate.
I recently heard from a movie-world friend who wondered why he's "perpetually excited" by the Oscar nominations whether or not he's impressed by the films themselves: "I've never been much of a sports fan, so I don't think it's the rooting part".
Gallbladder hematoma was impressed.
Impressed current cathodic protection (ICCP).
That really impressed my teacher...
