Gesture Drawing is one of the most mentally draining exercises for me as well, especially if you want it done well.
But that's why I do it as much as I can. It challenges me and makes me stronger at drawing so fast. It's something that's done purely as an exercise to help you improve. Just keep doing it and you'll adapt and be able to draw for longer. Keep doing it at 10 minutes. The next week, try 20 minutes. etc.
Because it's so hard, I usually do it at the beginning of my drawing practice session, instead of winding down with it. I also don't go for more than 60 minutes at a time, at most 90 minutes. I'd have to take like a 5 minute break.
Also, I recommend drawing at 2 or 5 minutes per drawing. That's enough time to get basic forms down with correct perspective. If I draw at 30 seconds, I just end up making stick figures with no perspective.
Good luck!