I have narrowed it down further and am pretty sure it's an issue with S-Gear (I've tried both v2.90 and v2.95) and certain DAWs. It occurs in Ableton Live and in Reaper, but does not occur in Bitwig Studio. I can get the dropouts to occur with a single instance of S-Gear on a single track and nothing else in the session. It occurs even if I remove all devices except for the amp (which cannot be removed), and bypass the amp at the bottom, so it essentially acts as a pass-through. It occurs regardless of which amp is selected. It doesn't occur if I replace S-Gear with (many) other plugins, even if the CPU load is much higher.
To really test it out, I put 25 instances of S-Gear on a track and set playback to a 1-bar loop. When the playback was set to loop, there were massive CPU spikes every time the playback head moved back, but when I turn off playback looping, the spikes (and dropouts) went away. You can see the difference in the attached CPU meter screenshot where CPU 1 is very spiky, but after I turned off looping halfway through it flattens out. This was taken in Reaper but Live looks similar. The spikes look small on the meter, but that is only because the meter averages over a window of a full second but the spikes are much shorter.