does it hurt the mag tube spring to be loaded?
 

on a pump action shotgun.

Does it hurt it to leave it loaded? Yes.

Does it hurt it fast enough that you'll ever notice it in your lifetime? No.

This gets kicked around all the time, guys swear it wears out springs (spring fatigue is a real thing, no question), and some guys even recommend unloading every day, or loading one or two less than a full magazine load... Mostly it's just conjecture. I've seen a 30yr+ old 870 that I know wasn't unloaded for longer than the time it took to reload it while shooting clays or after dumping a full mag of buckshot after coyotes near the feedlot for at least 25yrs that I recall. My uncle kept it in the back window of his pick up on the farm, always stoked full, until he passed away a few years ago.

If a guy is worried about it, buy a spare mag spring or two, just to have them on hand. If it's your defense weapon, you should be handling and practicing with it regularly, so if the spring would start to fail, you'd notice failures to feed at the practice range.

All that said, there are other bad things that can happen while leaving a firearm perpetually loaded that you'll notice before the mag spring fatigues.

ok thanks! just what I wanted to hear!

Just take that spring out every 4 or 5 years and grab each end and give it a stretch. I've been doing that with my Mossberg 500 since about 1985. Works fine.