I consider myself a fairly good developer, and I think that's in large part due to knowing, "doing this should be possible, and the reason it's not working right now is just due to stupidity (my own or the developer of whatever I'm using's)". But yes, in a few (thankfully rare) cases it just plain isn't practically possible. Even then, I've given up on problems just to have it nagging in the back of my mind and then randomly coming up with a beautifully simple solution weeks later. That's sort of the essence of what I like about programming (and math too).