I am surprised that you are having problems with your Dracaena. They are fairly bullet proof. You may be loving your plant to death. DITTO RBG and Imafan on the issue of water retention in the cache pot and the possible need to pot up in fresh soil.
I have a HUGE Dracaena on my patio. It is currently in a 24" pot. I pot it up every 3 years. The last time was 2 years ago - spring. In the process some of the branches broke. I stuck them in pots and they are now 3' + tall. There was a small piece - 3" - that I over looked. It was hidden in a bunch of pot shards. It sat on my potting table through winter with no soil. The following spring I found this little piece of trunk. It had roots and leaves, Stuck it in a pot. It is 2' tall.
Looking at the diameter of the pot in relationship to the height of the plant it could be root bound. There is also the issue of standing water in the cache pot as RBG pointed out.
Gently remove the plant from the pot. Inspect the roots. If they are wrapped around the root ball they are root bound. Unwrap and snip the roots. Loosen the soil.
If there are few roots and they are mushy then you have root rot from excess water. Gently rinse away the soil from the roots. Trim off mushy roots then repot in fresh soil.
Gradually move it to a location with more light.
Elizabeth - or Your Majesty
Living and growing in Lafayette, La.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant. ~Author Unknown