Losing two pints is roughly equivalent losing a liter of blood, which is about 15% of the total blood volume of six liters. That's actually quite easily compensated provided you drink some water and don't run a marathon immediately afterwards.
The problems I talked about before don't start until you lose more than 15% of total fluid volume, and the problem gets worse as more fluid is lost.
I found the following here:
Class I hemorrhage corresponds to a less than 15% blood volume loss and generally is well tolerated. Blood donors fall into this category. Treatment is oral rehydration or judicious use of IV fluids. These patients do have a diminished intravascular volume, but generally compensate well enough to have no classic physical signs of shock.
Class II hemorrhage is a 15%-30% volume loss. These patients generally will have tachycardia, anxiety and a lowered urine output. These are the first signs of shock. In these cases, prompt control of bleeding and resuscitation with IV crystalloid solutions are essential.
Class III hemorrhage is a 30%-40% blood loss. These patients will have a decreased blood pressure, tachycardia, minimal urine output and confusion. Such patients are unable to compensate for their volume loss. Control of bleeding and rapid resuscitation are essential to prevent later multiple organ dysfunction and death. This group of patients requires blood transfusion and may require surgical intervention to stop the source of bleeding.
Class IV hemorrhage is a greater than 40% blood loss and is rapidly fatal in all patient age groups.
So I guess it depends on how much blood is "a lot of blood" when lost to a vampire. Is your vampire character able to control him- or herself well enough to take less than 15%? If so, the victim will be good as new later that day. If it's more than that, things get dicey.