I really hate the idea that's been put forth that high school girls should be under trained so that they can see a bigger improvement in college. This makes no sense to me. Would you intentionally undertrain a football player or a basketball player so they would have a bigger improvement curve in college? Of course not; the whole idea is nonsense.
As others have said, what burns kids out is not mileage, it's the constant barrage of racing and hard interval workouts. There are some high school kids who run upwards of 30-40 races a year. Do that for four years and of course you're energy and you passion for the sport has been sapped.
For a girl who wants to run under 10:30, I would say you need to be in the vicinity of 40-50 miles per week. Obviously you should progress to this over the course of a year (or several years) and if she typically runs 20 miles a week you don't want to make that big a jump. But that will give her a solid enough aerobic base but not burn out. 50 miles a week is 6-7 miles a day, plus a long run once a week.
I would also say that you can avoid burnout by limiting the amount of hard, "go-to-the-well" type anaerobic efforts throughout the season. Clearly you'll need a couple of these, but most of the workouts should be fairly moderate. I would also try to limit her racing. No more than 4-5 hard efforts during XC, may 6-7 if you do indoor, and then another 6-7 during outdoor. That's probably a bit less than ideal, but assuming she's on a high school team that seems reasonable and less than other top runners.
Hope this helps, can you give us any more background on this girl?