Try doing something that interests you from the GMAT syllabus. For example if SC interests you more than RC does, then start with RC and then move towards SC. If verbal as such gets you sleepy, then do some tough quant problems which will keep you thinking. In case you're too sleepy, then just shift your intention of studying from studying for GMAT to just trying a puzzle kind of approach for few GMAT questions. Once you get involved, sleep won't creep in.
Another tip: When at times you're too exhausted, both physically and mentally, stop with GMAT preparation and read some articles from sources such as The Economist. While reading, try to observe the sentence construction and patterns, argument structure, why is the article written etc., By doing so you are in a way passively preparing for GMAT but on a much lighter note.
Hope this helps.
