Not familiar with that piece of equipment but very familiar with gear lash as I've rebuilt and repaired a lot of metal working machinery. Metal working machines must produce considerably tighter tolerances than woodworking tools but the adjusting knobs and related gear train are still much the same as you are currently experiencing. There's always some clearance in the gears, or somewhere in the gear train, usually by design. Unless yours is problematic (as opposed to just "unusual") I'd live with it.
I have the same issue when raising or lowering the blade on my table saw. Just enough play in the handle to irritate me when I want to back off just a hair. My solution to this particular condition is to back off more than needed, then raise back up again. This way I have the gear train tight and not subject to sliding back on its own (just a hair). I have the same condition on my joiner. Raise or lower the table and there's always a little bit of slack when reversing the wheel.
It's all very common.

 

I have a Delta drum sander and the 1/8 gear lash describes my experience, as well.

 

Thanks for the replies. Sounds like my machine is normal.

 

Both of my drum sanders (1 big Craftsman and 1 10-20 Jet) have the same gear lash as yours.

 

I have the Performax 16-32 which is identical to yours.

You can back off the tension on the four sliding bolts that connect the main drum to the table (the part that allows the drum to raise/lower). Only do this if you are confident at making these kind of adjustments. Too loose and the drum will rock, too tight and you'll wear out your jack screw.

Ideally the drum should lower itself when you screw the drum down (that is, the screw should not be forcing the drum down, gravity should). This setup will eliminate the backlash as the jack screw will always be loaded to one end. If getting the slide bolts loose enough to allow for this 'free fall' ends up letting your drum rock around, you can add an extension spring to help pull the drum down (makes the drum act like it is heavier).

Alternatively, as others suggest you can just live with it 8^)

Before I made my bolt adjustments, I'd always make sure to adjust the drum height in the same direction. That is, when sanding, I'd always lower the drum, never raise it, until the sanding was finished. If I changed grits, I'd swap out the belts but never change the drum height. For the first pass with the new grit, I would not change the height so in effect I'd get a light cut (this avoids an overly heavy cut on the first pass)