I agree with TTA. This just doesn't fit the noise scenario.
It has been a long time since I have seen generated noise turn a module OFF. I have had modules come ON during flicker/brownout conditions, but my experience has been that this problem went away when X10 added MOVs to appliance and lamp modules, back in the 1980s. If it is noise, a quick check might be to change the modules HC and UC several times and running the treadmill after each change to see if the problem goes away.
If it is noise simulating an OFF for that module code, or an "All Off" code, other modules would also likely be affected...are they? (set a separate lamp module to the same code and see if it turns OFF also).
What is controlling the light? Lamp module, Wall Switch? Wall switches are more sensitive to dips in line voltage.
What happens if you plug a table light into the same outlet as the treadmill, any dimming or flickering noted, when the light in question goes out?
This is a good one, but I don't think throwing money at filters will fix it. If you find a solution, please post it for us.