Are you locking your elbows as you get tired? Are you cocking your wrists backward as you get tired?

See if being aware of your elbow and wrist posture helps, and also move your hands around on the bars.

If the drops feel too far away, you can look into shallow drop bars. There are several good ones out now. Salsa makes a few very popular ones. You really want to be able to use the entire bar.