I definitely have had that happen! I think it's even more likely to happen on the SAT because you feel stressed and are under time constraints. It's almost like you think so much about needing to focus that you forget to focus. I've found that during the SAT, I realize halfway through a passage that I didn't really pay attention to the part I'd read and I have to go back.
What's worked for me is underlining not entire sentences but words and phrases that point to the tone or theme. In order to figure out the tone or theme, you're forced to pay attention to the stuff that's easier to pass right over, like figurative speech and, y'know, long and boring paragraphs. When I get to the one that's comparing two passages, I do my underlining as I read the first one, then stop and jot down a few of the main points or the theme or the author's opinion of the subject (they seem to ask about that a lot). That way, it'll be there to jog my memory when I inevitably forget the entire first passage after reading the second.
I also find that even in a silent room, plugging my ears with my hands helps me to focus more on what I'm reading and not be distracted by anything around me.
I'm not sure if these will help you, but they worked for me. Either way, I hope you find a method that works!