Another update. After a few more weeks of keeping the amps physical knobs at "not zero", the problem has not reoccurred. This when using the HD500X as the brain for my rig via Line 6 Link (using AES/EBU xlr cables). The problem never happens while plugging a guitar directly into the DT25's.
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Update to the update: The electric heaters were NOT the problem (info below). The issue happened again with the heaters unplugged. I *think* the issue is that I had the knobs on Amp 1 set to zero (except the master). My new theory is that the HD500X somehow was getting a knob control signal back from the amp and then dialing the mids to zero on the HD500X. Since the amp's knob settings are stored within the HD500X patches I don't think it should matter what the amp's actual physical knobs are set to, but perhaps it does actually matter. That said, I've set all the amp's knobs to 12 noon, reverb to zero, master set to given volume need. Haven't had the issue since. Fingers crossed.
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Update - the problem isn't just for this particular patch that features the Uber preamp. It happens on any other patch too. I figured out the problem. I can't explain why it happens, but I've discovered what is causing trouble. I noticed that the mid control would move to 0, all on it's own, at seemingly random times. On my Uber patch, the mid control has a drastic effect on the tone and volume. When the mid control would move to 0, the sound would get super muffled and quiet. On patches with other amps, the tone would just get "scooped" when the mids glided to 0... noticeable for sure, just not as drastic.
At first I thought I must have a controller or oscillator assigned to the mid control that was causing this whacky behavior. Nope. It turns out that the 2 electric space heaters' power cords were causing some kind of electrical interference. My rig is set up in my unfinished basement. It's in Minnesota and it's a bit chilly in the basement in January so I added 2 small electric space heaters to the room. Those space heaters are powered on their own electric circuit that is separate from my guitar gear's circuit. However, the extension cord used to power the strip used to power the heaters runs directly over the top of my HD500X's power cord and L6 link cables.
When I switched the heater's power strip off my whacky mid tone behavior stopped. Very very strange, but I'm glad the problem is fixed. I have no clue as to why it would just be a problem for the mid tone control. Weird, huh? Now I just have to figure out a better way to heat the room, haha.