First off I Highly recommend taking your drill to a Authorized Dewalt Service Center. However if you plan on doing work yourself, here is what I would look for.
If you don't have good contact between the brushes and armature you will get an arc of electricity. This can cause burning, and premature wear. When you pull the trigger, do you see a lot of excessive sparking?
Brushes do wear overtime and is usually a good place to start. If you've worked the drill extremely hard, I would check the armature for pitting. If the armature looks good, and your brushes are not completely worn down. Check the bottom of the brushes for pitting as well. If you see pitting (after the drill has been taken apart), I would recommend sanding the brushes lightly with emery paper, or simply buy a new pair. They are very cheap.
They will run you around $3.00 Dewalt Part number's N031376, N031377.
Here is a look inside the Dewalt DC720, identical drill without the hammer function.
http://dewaltownersgroup.com/index.php/topic,27.0.html