What do you suggest if my limbs fall asleep quite often?

An apple a day: I'm assuming you mean they fall asleep often after prolonged positioning, as this is probably the most likely cause for your symptoms. Those who are thinner also tend to be more susceptible to this. Adequate diet, sleep and physical activity would be beneficial in maintaining good overall health. Vitamin D and iron supplementation if needed. A routine checkup with PCP could help sort things out.