It's said that the battles SuperAlloy Darkshine lost was due to running out of stamina , not because his physical body was damaged. Is this true? Can SuperAlloy Darkshine be hurt?
Said by whom?
The only fight you see Darkshine have in the manga at this point is against Bug God, which is an easy victory.
In the webcomic, he suffers a psychological breakdown in his first fight (ending in chapter 76) against Garou when the thought that he might lose occurs to him. Even then we see him bleeding from his mouth and nose. In his second fight against Garou (chapter 85) he is easily knocked down, has multiple minor cuts and a head laceration at least, and ultimately can't even get one word out without coughing blood before passing out. He's not explicitly shown or stated to have any broken bones, or anything more severe than any of that, though the coughing bit suggests he might have fractured ribs. He ends up knocked out and unable to continue fighting in pretty short order, one way or another.
Before all that we're told he had never lost a fight before (chapter 76; as a hero at least; before he started training maybe he'd been in a school fight or something and lost), and never really felt challenged.