hi~
Sucking, swallowing and breathing (SSB) are complex processes, even when considered separately. When an infant is fed, these processes must work together smoothly and efficiently with highly accurate timing and coordination to result in safe and efficient feeding. If he is only drinking 2 minutes and then sleeping it is a sign that he is exerting too much effort thus having a hard time with the SSB process. He needs to build up his endurance.
Have you tried :
1) to support his chin and cheeks (so he has to work less)?
2) providing with this increased body support (so he doesn’t have to work on his trunk support while feeding)
3) pumping prior to feeding in order to stimulate milk production?
Also it is okay to be in a quiet alert state, but he should be re-alerted when he becomes drowsy. Alertness is critical to an infant's ability to communicate with the feeder regarding loss of suck-swallow-breathe coordination. Infants can be alerted by using a burping maneuver, such as patting or rubbing the back. Unswaddling a blanket (or removing blanket that is covering him for a few minutes lets "fresh air in." Before resuming feeding, rub the infant's head, take its t-shirt off and put it back on, and if you are swaddling him - reswaddle him.( http://speech-language-pathology-audiology.advanceweb.com...)
** Avoid prodding him. When you breastfeed, avoid twisting or turning the nipple, moving it up and down, moving it in and out of the infant's mouth, or jiggling it. While the intent is to help him, it may lead to safety issues. These techniques result in fluid passively entering the mouth without the infant's active participation. The risk of aspiration significantly increases because the fluid may overfill the oral cavity and move toward the airway. Until the infant actively swallows, which occurs only after active sucking, the airway is open and in jeopardy. Thus if you do this and he falls asleep he maybe sleeping with fluid in his mouth putting him at risk for coking. (http://speech-language-pathology-audiology.advanceweb.com...)
Does he do the same thing with the bottle? (drink for a couple of minutes and then fall asleep)? Have you had a lactation consultant assist you in the beginning (if not you may want to see one). Another option is seeing a therapist who specializes in breast feeding (some NOT ALL occupational therapists or speech therapists work with assisting parents with breast feeding - are you near CHOP? they may have therapists who specialize in breast feeding). If you decide to see a therapist make sure when you schedule an evaluation that you ask for someone with experience in breastfeeding and premature infants - some therapists who work on feeding have not worked on breastfeeding.
hope that helps! Good luck!