She may have mastitis, so it's painful for her when they approach the udder. Check how the udder feels, is it soft and pliable, or hard? Warm, or hot? Healthy pale pink or red?
It may be that the udder *looks* full but is in fact empty, so she's just telling them to leave her alone, there's nothing there for the moment.
If neither of those things, she may also be managing the lambs to make sure they all get a fair share. Or, she knows she doesn't have enough for all 3 going forwards and she has selected the one she is going to sacrifice.
Put different marks on all 3 lambs and see if it's always the same one she butts, and whether she ever lets it feed. If she never butts the other two and lets them feed, always butts the one and never lets it feed, then it's likely she knows she can't keep all 3 going. Remove the one she's decided to sacrifice and rear it on the bottle. And watch out for the same thing happening again if she gets to a point where she can't manage 2.
Personally, any ewe which has grown and birthed 4, even if one was dead, I would not leave 3 on her, it's too much. Unless she is in cracking condition, I might even only leave her with one, so she can make a good job of rearing that without too much further drain on her system. I have lost lambs, udders and even ewes by leaving 3 (or even 2) on a ewe that wasn't up to it, even with additional feeding and the best grass.
At the very least, I would be topping up the lambs from a bottle to ease the load on the ewe. If you can get at least a litre a day into them between them, that reduces the load on the ewe to more like twins. I see you have tried to top them up but they weren't interested. Either take one off or keep trying with the bottle once or twice a day; if she is starting to not have enough milk, they will eventually get hungry enough to want the bottle. Hopefully before they damage her udder.
Maybe consider not flushing your ewes next year to try to reduce the incidence of quads and triplets.