Improve your accuracy and reading skills of different patterns and overtime as you play faster maps you'll adjust and build up your stamina. If you're burning out mid song you might've jumped the gun on the difficulty. I would only say its understandable to start burning out in a song if its the literal last seconds or the peak of a song, and if it slows down your good to keep playing well if you pass that.
(Make sure not to strain yourself too much. You don't want RSI Issues.)
My path wasn't the most time efficient but I backtracked from high 4's to low/mid 4's and started practicing my accuracy instead of HP passing higher and higher starred maps with High B's and barely 90's. Going back and getting 97+ on slightly lower star rating maps helped me realize I was semi mashing through certain patterns instead of actually learning how to play them. It overall helped my accuracy a lot and in turn cleaned up my reading/muscle memory with patterns I couldn't do well on before.
I'd also recommend to you before pushing for these higher star plays you warm up. Don't jump right into a map that you know will require a lot of stamina from you. Ease your way into it and good luck! o-ob