Broken capillaries on face is sometimes a symptoms of Rosacea, which causes your skin to flush and become red. Age. Broken capillaries on your face are more prominent as you age, as your skin usually gets thinner, which makes it easier to see the veins.Excessive alcohol intake. or smoking. Chronic alcohol intake can increase blood pressure, which makes the veins in the face to enlarge.roken capillaries on your face are more prominent as you age, as your skin usually gets thinner, which makes it easier to see the veins. Excessive alcohol intake. or smoking. Chronic alcohol intake can increase blood pressure, which makes the veins in the face to enlarge.