I'm no expert, but I have the same issue with my 6 week old. He does fine for a while, but gets frusterated when there isn't "quick milk" anymore. After 2-3 let downs on one side, I put him to the other side and he seems to do fine. Have you tried pumping and watching your milk come down? I've noticed that the milk has different consistencies for the foremilk and hindmilk. In my case, the hindmilk comes in pretty quickly after the letdown, then there is no milk at all until the next let down. Each let down seems to take a bit longer to come. After 2-3, I seem to lose his interest. Try to pump for 10 mins and watch what happens... it is very interesting and you learn a lot about how your milk works in your body.
I also noticed that the nipple gets a lot softer after he's been nursing on it. It makes it much more difficult for him to latch back on... I think he has a harder time "finding it". This was a huge problem when he was 2 weeks, but is much better now. I found if I pinch my areola right behind the nipple to make it stick out more, he "finds" it much better. Once she has found the nipple, you need to release and then massage higher on your breast to start the flow again. If you massage too low or keep pinching, she'll lose the suction on the latch. You may also want to try that before switching sides.
Finally, how long is "a while"? Are you getting just a few minutes on a side, or more like 10 minutes? Is the sucking different? My ds will suck about the same amount of time on both breasts, but the second is a much slower suck/swallow combo. It's more of a lingering thing than it is the hunger fufillment!
If you do both breasts, just be sure you start on the one you left off on the previous feeding. For example, if you started with your right breast and then moved to your left breast half way through, the next feeding should start on the left then go to the right. Le Leche League has more info on that if you want to look it up.
Good luck!
