Getting close to the work that you create is essential to ensuring that you are producing the highest quality result possible. This doesn't have anything to do with love, or attachment, but rather the level of focus that you apply as you work.
Here's how it works... Each time you hit a milestone in a design (or illustration), do two things (mentally, not literally): First, step back and look at what you've produced so far and see if it meets the expectations of the project as a whole. Second, Look deeper at the details of what you are creating and ask yourself honestly "Is this the best I can do?". It doesn't take long, and shouldn't affect your scope that much, considering what you may learn from the experience.
Sometimes what you see in terms of quality is difficult to deal with, but learning how to sharpen your eye on seeing the weak spots in your work will improve your style exponentially.
Why bother? You are not the only person who can do what you do. There are others, and right now, somebody is trying to become better at their own work, possibly leaving you in the dust. Most importantly, the pride in knowing that the work you did is work that you won't be embarassed to share with the world.
So get close, tweak the fine details, and make your pixels happy.