TLDR: Make sure you have fresh air in your marathon meetings!
Buy an air quality indicator and take that into the room. Vent the room when it indicates too low O2 or too high CO2 levels. Meetings are often held in crowded rooms and people often forget or don't dare to open windows during the meeting. Insufficient air supply/over-saturation with CO2 makes you tired. It might just be that your colleague is more susceptible to it thenthan the rest of you.