I have had the wheel now for a few months of sustained use and it clearly has become loose in the steering column. I have talked with other users who have experienced the same thing. If I have the wheel mounted firmly, the wheel and column move up and down a good quarter inch within the enclosure.
I have taken the wheel apart a few times trying to fix it and it seems to come down to the fact that the shaft the wheel connects to just rests loosely in a socket. I am not smart enough to figure out a way to tighten up the shaft in the socket short of a ball bearing system (and I am not smart enough to figure that out either). :)

Does anyone else have this issue? Has anyone found a solution? I will post some pictures later of what I see to be the problem area.

Are you saying that by pulling down on the wheel during racing, lets say, you are physically deforming the plastic enclosure that holds the shaft in place?

I'll do some searching as I read about a fix for your problem(a few weeks ago). The fix entailed using a bearing to add support.

Here you go.
http://www.andrewdorey.com/default.aspx?p=360wheel

I found it on the xbox website when trying to decide if I wanted to buy this wheel or not. The "wobble" seems to be a somewhat common problem.

Here you go.
http://www.andrewdorey.com/default.aspx?p=360wheel

I found it on the xbox website when trying to decide if I wanted to buy this wheel or not. The "wobble" seems to be a somewhat common problem.

Awesome. This is exactly what I was thinking.

Looking into the wobble further, it seems to be the source of gears getting out of whacking causing them to slowly strip over time. It seems that upgrading with a bearing is a good way to increase the wheel life.