I agree with Sara, as I had the same problem too. I would recommend talking to a Board Certified Lactation Consultant just to rule out any supply problems. It is not a very common problem, but can cause a baby to act the way you describe.
With my first, by the time he was five weeks old, he was literally nursing for hours on end – all day, all night. Other moms advised me that this was normal, or that he was a snacker, or that he was using me as a pacifier, so I just thought it was par for the course when breastfeeding and just went with the flow. By the time he was six weeks, I really felt like it wasn’t normal. I could not get him to take a pacifier, and if he was not on breast he would just scream and scream. I tried everything to distract him and soothe him, but he just wanted to nurse. I thought "you can't possibly still be hungry!"
Turns out, he was literally trying his little best to stimulate my milk production, and it just wasn't working. He would fall asleep on my breast because he was so tired of sucking, but then wouldn’t sleep long because he was still hungry. I had a pretty intensive session with a lactation consultant and she could tell by various symptoms that I simply was not producing enough milk for him, and she advised me to supplement with one formula bottle a day. And, it worked. It satisfied his appetite, and then he was able to nurse normally the rest of the day, getting what amount I was able to supply. I think if anyone else would have told me to give my baby formula, I would have balked (actually, my DH was the first to suggest it, and I chastised him) but coming right from a lactation consultant, I knew it was the right thing to do.
I am not saying to start giving you baby formula right now, but I would recommend a session with a lactation consultant just to be sure it is not a supply issue like mine. Trust your instincts if you feel like something is wrong, no matter how many people tell you if is perfectly normal.
BTW: She could tell it was a supply issue based on a combination of things. None of these alone are cause for concern, but when combined can identify a supply issue:
1.I brought baby to the appointment hungry (and screaming) and the LC weighed him before and after a full 30 minutes on each breast, and he had only transferred 1 oz of milk
2.When my milk “came in” I never got engorged or uncomfortable
3.Baby was gaining weight consistently since birth, but was on the low side for normal weight gain.
4.Baby’s behavior of nursing for hours with little break between nursing sessions