Hi Volen, it's because fillets will shrink to a very small or 0 size when 2 surfaces become smooth to each other. Situations where 2 surfaces come very close to being smooth to each other tend to make filleting difficult because the fillet becomes very small and it's difficult to use a tiny surface to intersect and trim against other nearby surfaces.
Here's a more visual demonstration of this, here are 3 different instances of surfaces meeting at different angles, and all have been filleted with the same fillet radius:
So the way a CAD fillet works is that it constructs an arc between 2 abutting surfaces that is tangent to each surface. All the arcs shown above are segments of the same radius circle, but on the sharper angle a longer length arc is needed, and you can see as the angle decreases and becomes shallower the length of the arc becomes shorter and shorter, it is still a piece of the same radius circle but using a smaller and smaller piece of that circle.
Now, imagine the surfaces are totally smooth to each other  at that point there's no length of arc left that will fit in there at all. In a situation like you've made there where surfaces come quite close to being smooth to each other it also means that the arc size becomes very short or even 0 in those places and that will tend to make it difficult to fillet. Filleting requires many complex steps of operations such as computing offset surfaces, intersecting offset surfaces, extending fillet surfaces, intersecting fillet surfaces with each other, and building corner juncture patches where fillets collide into each other. Many of these operations are difficult to calculate on a tiny sized fillet surface.
> what are good general methods of working to ensure that filets and most operations will work
Well, for filleting you will want to have surfaces that meet at a more distinct angle rather than coming very close to being smooth to each other where they meet up. For your situation you'd probably plan in advance that filleting is not going to work there, and trim away some space between the surfaces and put in a Blend instead.
Hope this helps!  Michael
