Final answer:
The patient's clinical signs after fluid resuscitation indicate a state of fluid-refractory septic shock, which means their cardiovascular system is failing to respond to fluids, necessitating additional treatments like inotropes or pressor agents.
Step-by-step explanation:
The symptoms described for the 7-year-old patient - capillary refill of 3 seconds, diminished pulses, narrow pulse pressure, and cool, mottled extremities after administration of three balanced/buffered crystalloid fluid boluses - are indicative of a type of septic shock. These clinical signs suggest that the patient is not adequately responding to fluid resuscitation, a condition termed fluid-refractory septic shock. In this situation, the patient's cardiovascular system fails to maintain adequate blood flow and oxygen delivery to tissues despite fluid therapy, necessitating further interventions such as the use of inotropic or pressor agents that will help to raise blood pressure and improve tissue perfusion.