This happened to me too, during practice tests. I think it is not so much a stress problem as becoming better at actively reading, especially when you are a somewhat lazy reader like me that is used to "skipping over" what doesn't make sense until you get to a part that you do understand and then using context clues to get the hard bit. With LR, you don't always get to a part that is "easy to understand." SO, my eyes would "skip over" the whole damn thing...i.e. "glaze over." I found I had to practice slowly, then build up to my normal fast reading. I assume you are re-taking in December...plenty of time to work up towards 30-minute LR sections.
This actually happened to me too during the test this past Saturday where I would read but didn't know what I was reading...and I honestly felt horrible after the test. It wasn't until the third section that I started to maybe comprehend what I was reading. I think it's a mix of nerves/stress (my heart was racing a mile a minute) and also I am not a fast reader to begin with so maybe both of those combined for the best of us. For people like us, all I can say is don't give up. I've wanted to go to law school since high school and I felt like poo (and still do) after this test. I will most likely take it again in Dec. too. Hang in there...
When I studied and took the GMAT I had the same problem. For the test what I did wastell myself, at the start of every question, "This is the only question on the test". This prevented me from thinking ahead or behind or worry about my timing. This worked for me and eliminated “man I have read this three times already”. If you are going to a doctor you may want to consider a sports psychologist or a hypnotist since this sounds performance related.