HP is a function of RPM x Torque. HP= (Torque x RPM)/5250. So the short answer is yes, as you dial down the speed the HP drops off. A 3450 RPM motor has half of the torque of a 1725 RPM motor of the same rated HP.
I like where you're going with that and I'd like to expound a bit for/to Brian..
Let's say we hooked up that 3450 RPM motor to a lathe and fed it 230V 3phase from mains. No work piece in the chuck, just free spinning at rated RPM. Are we getting 1HP out of it? nope. We might be getting 1/10th HP from it. It's not until we chuck up a big bit of metal and start mercilessly gouging into it with a pointy object that current starts to rise and torque starts to rise, and thus HP ((
torque x RPM)/5250) starts to rise. When we gouge into the workpiece hard enough to make the motor draw 3.2A, that's when we know we've hit 1HP.
So, let's say we empirically discover how aggressive of a cut it takes to draw the rated 3.2A @ 230V (1HP) and then we take that same depth of cut repeatedly at slower and slower speeds... would you expect the "diminishing HP" to eventually cause the lathe to bog down and come to a stop? I wouldn't. I'd expect to be able to maintain the same cut almost to zero speed, because my torque isn't changing, just my speed is; and that's the reason for the "diminishing HP" ... diminishing
speed ((Torque x
RPM)/5250). (example is not perfect; real world observations subject to change in behavior of cutting action per feeds & speeds and also effects of electrical characteristics in the motor which I don't trust myself to explain accurately)
So yes, you "lose HP," but no, you don't really "lose" anything that you would miss. Kinda like how a car can be rated 245HP but only require 25HP to maintain freeway speed - set your cruise control and you'd never know that those other 220 ponies were asleep in the stable.