The spring the recycles the slide. I don't remember what it is called.
Ah. Recoil spring.
In general, the recoil spring is compressed just sitting in the gun. Cocking the gun compresses more the spring only briefly, and when the slide returns to battery (once the gun is cocked), the spring is then returned to its "slightly compressed" situation.
Leaving it that way technically will fatigue the spring, but only if you leave it that way for a couple hundred years or so.
Firing the gun and making the recoil spring work through many full compressions is far harder on it, and will (over time) fatigue the spring such that it will not expand to its formerly full length.
Modern magazine springs are the same. If you leave a magazine full of ammunition, it will be MANY years before it is unable to do its job. (Matter of fact, corrosion and damage due to atmospheric moisture, spills, banging the magazine around, etc, will cause more problems than simply leaving the magazine loaded.) What fatigues magazines is actual
use. People who shoot a lot have to replace magazine springs MUCH more often than people who simply leave their magazines loaded all the time, but don't actually shoot.