I had a friend in track last year who actually encountered a similar problem. Similarly, his blood pressure would increase than suddenly begin to drop after he had elevated his heart rate to a certain point. What he had found (from consulting his personal doctor) was that the diameter of the veins (arteries, capillaries or whatever - specifically in his legs) increased and as a result the pressure within his blood stream decreased. This makes sense based on physics - continuity equation - Area(1) * Velocity(1) = Area(2) * Velocity(2)
By making sense of this, you might understand that if your Hear Rate remains the same, the only way that your Blood Pressure can change is if the volume somewhere within your bloodstream changes - as did with my friend. He was a distance runner and after races he would practically faint because the diameter of the veins in his legs increased so much that his blood pressure dropped significantly. Not to scare you. And I'm not a medical professional so...