can't keep baby awake to eat at night

My baby is just about 5 weeks old. We have been feeding, sleeping, everything on demand. Some nights she does pretty well. She pretty much consistently wakes every 2 - 2 1/2 hours and usually goes right back to sleep when finished. The problem lately is that when She wakes up to eat and I sit to breastfeed her, she almost immediately falls back asleep. I can't get her to stay awake long enough for her to eat enough to stay asleep! I've tried stripping her down to her diaper, blowing on her face, tickling her face with my hair, tickling hands and feet, cold wash cloth or wipe on her face, belly and back. I pick her up, change her diaper, switch sides, burp her. Sometimes one of these will work but mostly it won't. So I end up putting her back to sleep, falling into bed and then being woken up a half hour later again cus she's still hungry. The last couple nights she wakes up every half hour and seems to fuss a lot at night and fall in and out of sleep. Anyone have this problem? I get so exhausted, I just wanna give up and put her back to bed. Cus 30 mins of sleep is better than no sleep.