I learned about the importance of ample amounts of Timothy Hay in bunny diets when our own bunny, Russell, was rushed to the emergency vet because he stopped eating due to a condition called Gastrointestinal Stasis.
Russell also has a condition called Malocclusion, in which his teeth are slightly misaligned. I suspect this misalignment didn't allow Russell to properly chew his rabbit pellets, which then got blocked up in his stomach, causing the Gastrointestinal Stasis.
Russell's current diet, on which he thrives, is 95% Timothy Hay and 5% fresh organic field greens. With regular tooth clippings keeping his Malocclusion in check, he is now a very happy bunny!
Here's some more information on proper nutrition for rabbits from Dr. Sam Munn of the Greenwood Park Animal Hospital. In my opinion Dr. Munn's clinic is one of the best in Toronto for treating pet rabbits.
A happy Russell.