My DD was born at 32+6 so similar gestational age to yours. She was in the SCBU for four weeks, and they took her feed tube out about a week before she went home. Prior to the tube coming out, she was on a combination of tube feeds, bottle feeds and breast feeds, and even when she went home (at 37 weeks), the paediatrician told me to supplement her breast feeds with the bottle as she still wouldn't have enough energy to get all her needs from breastfeeding alone.
Like yours, she wasn't able to breastfeed for more than 30 seconds or so at first. I remember the nurses saying that the sucking mechanism kicks in around 35-37 weeks, and that is actually the reason that hospitals now deem 37 weeks to be 'full term' - because by that age most babies should be able to feed on their own (it used to be that anything less than the full 40 weeks was considered premature). IIRC, I think 36 weeks was about the time she started to get the 'hang' of breastfeeding, and was able to feed for a few minutes at a time. I do remember something just sort of clicking then - even though she was only able to feed for very short periods, I could feel her latch just suddenly felt 'right', instead of shallow, and it was like she was really getting the milk this time. My supply improved no end just from those few minutes of feeding. By the time we left the hospital she was doing full feeds, although she often fell asleep suddenly in the middle of them, like an old drunk 
The thing to remember about preemies is, as another poster pointed out, that they aren't supposed to be here yet - they are meant to be in the womb. So of course they can't feed for any length of time, and that's why they just want to sleep the whole time, and they barely even cry. (I remember what a shock it was when my DD suddenly developed a full-throated newborn roar right around the time she was due to come home, after my being used to her just mewling occasionally like a weak kitten
) But the other thing is that they change SO quickly. Literally every few days new skills and strengths are 'coming online', so I wouldn't be worried that yours can't feed for long now. It's great that she already has a good latch - that's most of the battle.
Btw, every mother of a preemie that I know has struggled with milk supply issues, even after their babies get older and stronger. IMO nothing can make up for those lost first few weeks, which is when baby is supposed to be feeding constantly and your supply is really established. I pumped assiduously since DD was born, and she eventually became a strong feeder, but it was always an uphill battle to make enough milk and we always kept a tin of formula on hand. A friend helpfully gave me some breast pads, saying they had saved her from many embarrassing moments, and I never needed them! Never had issues with overflowing breasts. Quite the opposite 
I second Malva's suggestion to hire a hospital-grade breast pump if you haven't already. The home ones just aren't powerful enough to keep up your supply while your baby isn't feeding. Also, and this is a bit random but I thought I'd mention it: anecdotally it seems like prem babies are more prone to developing reflux, possibly due to having the feed tube in for so long, so keep an eye out for that and get it treated ASAP if it becomes a problem. My DD developed terrible reflux and that was the main health issue we had once she came home. It was OK once she got proper medication though and it cleared up completely soon after she started solids.