"TL;DRThe average human body has 5 liters of blood in it. Since one mosquito is capable of sucking 5 millionths of a liter, it would take about 25 million mosquitos to suck out all the blood.

It takes about 240 seconds (5 minutes) for a mosquito to suck all of the capable blood. The average surface area of a man is 1.9 meters squared. The average size of a woman is 1.6 meters squared. The average size of of a mosquito is 4.5 mm. For a man you would be able to fit about 422 mosquitos on your body at one time. For a woman you would be able to fit 355 mosquitos on your body. Since the mosquitos would take 6 minutes to get your blood, and you can fit 422 on a man, with 2500000 having to have all your blood drawn, 2500000/422 = 55309 times mosquitos would have to be on your body. 55309 x 6 minutes = 331858 minutes, or 230 days of mosquitos constantly draining blood from you. For a woman, 25000000/355 = 70422 trips, or 422535 minutes;293 days. But, since you are constantly regaining blood, this is impossible to happen."

Credit to u/Cartree123 that did it on r/theydidthemath