You can remove the dead stalk, but! Make sure it is TOTALLY rotted before doing so or you will pull up part of the healthy plant (I have several of these suckers, have had the rotted stalk thing a time....or two)
These guys don't take a lot of water, another thing that is a major downer for them is a type of soil that retains moisture, if the water sits on top when you water for any amount of time you will want to change to a better draining soil. Another thing I did, not sure if this helped or not was I removed all those nasty bread ties that were cutting into the trunks (why do they do things like that?) Out of the two that I had the most trouble with I have 3 stalks left on each, and they have been growing like gang busters. Hope I helped some:)

Thank you so much! Ya, I just took out the dead stalk and it was all grey and dead inside and the part of it under the dirt was moldy and gross. I also mixed some sand with the soil so hopefully that helps too.