My daughter was born three weeks early and had a case of "sleepy baby syndrome". She slept all the time, even through feedings. So we were told to wake her up for her feedings and to keep her awake during them. I can tell you that it wasn't an easy task. However, I did learn a few tips that I can pass onto you.
Before giving sleepy baby advice I want to give a couple additional helpful tips. What I want to say first is that if your baby is losing weight because of "sleepy baby syndrome" then you need to be careful about how often you are feeding your infant. Make sure to wake baby quite strictly every 2-2.5 hours from the *beginning* of the last feeding. Also keep in mind that you can supplement baby with pumped breastmilk using a syringe or spoon if needed. You do not have to use formula as breastmilk is higher in calories than formula anyhow. Sometimes a Pediatrician will push formula as the solution to this problem but I can promise you there are many other options. Additionally you are typically allowed one 4 hour stretch of sleep at night.
Waking a Sleepy Baby and Keeping Baby Awake while Breastfeeding:
1. Change baby's diaper. This is always the best first thing to try. It often works and it is nice to keep a fresh diaper on a new infant anyhow.
2. Hold baby upright and rub baby's back.
3. Strip baby down to diaper.
4. Gently scratch or rub baby's head, ears, feet, or back.
5. While feeding use breast compressions. This is where you squeeze your breast above the areola, gently and in slow repetitions.
6. If all these steps fail you can put a damp washcloth or diaper wipe on baby's feet.
7. When every step above fails some parents resort to washing baby's face with cool water. This is something that only should be resorted to after you have repeatedly tried the above steps. It is not pleasant for baby and is only a last resort.