That's weird. So, I went to Training Mode, grabbed Bowser, and I jabbed at him. You're right. Samus can only cause damage to him once. All the rest causes no damage. Strange.
All right, now I didn't even inflict damage on him. When I tried it again, then I did 2% damage on him. After that, I grabbed him once more, no damage was inflicted on him. Now it was 3%. How many more times am I going to have to edit this?
I think I found out the problem. Bowser is grounded. I got up to 4%, the normal amount of damage you can give an opponent if he or she begins at 0%. I moved Bowser over to where the edge was at, and when I grabbed him, he was not on the ground, but was still held by Samus. When I did this, he received more damage.
Problem solved.
Yay! I gave him 5% damage.