The problem is that live binding will only work with Observe.Lists. _.filter is returning plain Arrays of Observes, so the Observes are still updated, but if you add more items to your original list, the Arrays have no way of knowing they should update. I've created a simple example to hopefully inspire you and show you that this sort of thing can be done in an easy way using Observe.List and computes.
I would encourage you to transform your list so that each section has a questions array which has an answer array similar to how this groups items by company and gives you a list of sections with an items array. You could actually use groupBy twice, once on the ungrouped list to add all questions to sections and again to group all answers with their question.