One month old having poor nursing sessions?

When my one month old nurses, she drinks from one breast for about 7-10 minutes and will then fall asleep. When I go to put her down, she'll wake up shortly after and cry, so I nurse her again. Is this normal? I try to keep her awake to nurse more fully but she can't seem to stay awake. It always takes us at least two sessions before she gets full and falls deep asleep.