i had the exact same problem with my now 4 month old, the first month was just like you were explaining, he was only awake for about 2 hours during the day! and i had to keep waking him up every 2 1/2 to 3 hours to feed. as he was almost 4 weeks early, i had to make sure he was getting plenty of milk.
i did find that if i took all of his clothes off, and just fed him in his diaper, and when he started to fall asleep, open up his little hand and rub his palm, it seemed to keep him awake enough to get through a feeding. hope that helps!
now that he is 4 months old, he will only wake up once during the night (between 8:30 pm and 6:00 am) which i find unbeliveable, considering my first 2 children didn't sleep through the night till well into their first birthdays! He still sleeps quite a bit during the day but around 3 in the afternoon untill 6:00 pm he is usually wide awake and babbling and kicking up a storm.
hope it helps