Supposedly blood pressure may fall due to a systemic infection (a long the lines of sepsis). What is the reason for this?

Toxin release. Many bacteria are capable of creating chemicals that act as toxins, disabling the system the blood vessels have to maintain tone (or the squeeze) within their walls. Once the vessels relax the pressure falls. Doctors have medications that counteract this effect that are called pressors agents.
Vasodilation. Low BP is due to vasodilation leading to low peripheral vascular resistance.