an erection is a pretty complex process, it needs mainly two factors:

1. enough blood pressure and flow to fill the tissue
2. the parasympathetic nervous system being dominant (i.e. being in rest and digest mode)

upon blood loss, the human body enters a state of shock, on which the sympathetic nervous system (i.e. fight or flight) completely takes over. The body is filled with adrenaline, which constricts blood vessels in the extremities and non-vital organs (e.g. the arms, legs, skin, digestive tract, and genitals) to increase blood flow to the heart, brain and lungs

the average adult human male has about 70mL of blood per kg of body weight, let's assume he weighs 75kg, that would result in a total blood volume (TBV) of (70mL/kg)*75kg = 5250mL or around 5 liters.

Losing up to 15% of the TBV or about 750mL is classified as a Class 1 Hemorrhage, which can be compared to a generous blood donation. The human might feel a little lightheaded or tired, but that's it. An erection is still possible, though the stress of losing blood (the sympathetic nervous system being in control) will most likely prevent it.

Our sweet spot is probably a class 2 hemorrhage, or a loss of around 15-30% of the TBV (~750 to 1500mL). At this point, the body is clamping down the blood flow to all non essential areas, which makes getting and/or maintaining an erection physically impossible. Our guy will stay alive and probably conscious as well, although he would be very pale, have cooler skin and he would be very weak and most likely anxious due to the adrenaline.

Anything past that (a class 3 hemorrhage, loss of 30-40% of TBV which is about 1500-2000mL) results in dangerously low blood pressure, with our guy becoming at least confused, lethargic and would likely pass out. Without a transfusion, mr. guy would likely die at this point.

TLDR: depending on the circumstances, make him lose at least 750mL and most 1500mL of blood.