I mentioned in a recent article that someone once told me that when someone tells you they are too busy to do something, it's because something else takes priority over you. This could sound very offensive (and might be depending on the situation), but at the same time, it's a very real definition.
Think about this. If you just had kids, your new schedule will be a priority over friends. If you have a new job, you'll need to get acclimated and friends may take a backseat. This doesn't have to be forever, but if someone tells you they are busy you need to understand that that's just the way it is sometimes.
I'll use myself as an example. As a freelance writer, I value the friendships I have with other writers in my area. I try and attend lunches and get-togethers, but my job takes priority. I try and keep up with everyone and attend events when I can, I make a real effort to clear my schedule and do this, but even with that there are some times when things just don't work out and I can't be there.
The key to determining if a friend is blowing you off constantly and not acting as a friend is how much of an effort they make. Maybe they can't be there all the time. Maybe they try but if you want them to be a best friend, it's just not going to happen. This doesn't mean you can't be friends with them, but you need to decipher what the busyness excuse really means and it probably changes from friend to friend.