Keeping Up with the Reading
That's the main challenge about graduate school: There's so much more reading and it's never done. Not only will you read for your classes, but you'll also read independently for your own research. It doesn't really get better either in the sense that after graduation you'll still have a ton of reading to keep current. Though of course no one will embarrass you in class for not having read!
There aren't any easy answers, but here are some links that may be helpful:
Reading: Improve Your Comprehension and Efficiency


Comments
One thing that can help is getting the readings in advance. Between semesters use that time to read.