If I start a shooting session and my draw time is off, and there is no good reason for it like injury, illness, or fatigue, it's almost certainly because of tension. More than likely I've had a rough day of work and chugged a Monster on the way to the range. In my experience shooting with or teaching others it's a common issue.
The next time your draw is slow hit the start button on the timer and then take note of how you feel before the beep. Tension in the back, shoulders, and arms is common. You may feel your shoulders are shrugged. If so, relax. Take a breath, hum a relaxing song, rub your ears and say woosah, whatever works for you. Then see if your draw speed is back where it should be.