And it immediately makes me think that it's the aerobic part of your system that needs working on. Once you get to 3+ miles, you're in the territory where anaerobic fitness (though still important), isn't key.
Reading between the lines of literatin's post above, I'm sure she too is wondering if you're getting in enough slow miles in to build up that aerobic fitness.
At least one run a week, 10 miles or longer, at a pace more than 90s per mile slower than your 10K race pace. Plus one other slow run too.
Presuming your aerobic fitness is not up to scratch, it would probably pay to work intensively on it for 6-8 weeks. Just have one speedy session a week... and concentrate much more on lots of slow (boring?) miles! That shouldn't cost you much in anaerobic fitness.. but would give you a much better base from which to improve.