It takes muscle to carry a slower pace.
I have to disagree with running her down. At a show, that just makes you look bad as a rider, and it'll leave her tired, which isn't impressive to look at in a class, and she has no way of recongnizing what it is you want, as there's no release, so she won't learn a thing.
I'd suggest a lot of rating. Push her up, slow her down, push her back up, then down again. She should go the pace you set for her. Make sure she's moving correctly through her hind end. Without hind impulsion, the lope is nothing.
When she achieves a slower pace, after a couple of strides praise her, let her stand for a second, and give her a break. She needs to realize that going slower is what you want. That will come with releasing and rewarding at the correct times. Over time, as the muscle builds, she'll be able to carry a cadenced lope around the arena for several minutes without fault.
I'm telling you now, give yourself a good year to get to that point. Set a year as your goal for a killer lope, and go from there.
There are others around here who can explain this better, so I'll leave that to them.
"You're just as sane as I am."~Luna Lovegood.