Getting the blood drawn does not invalidate the fast. As a matter of fact, the Prophet got his blood drawn when he was in ihram and while he was fasting. (Bukhari, Medicine, 11, Hunting, 11, Fasting, 11). Moreover, the Prophet said: “ There are three things that do not invalidate the fast : getting the blood drawn, vomitting, having a wet dream”. (Tirmidhi, Fasting, 24)