I think I've found a solution.
The root of the issue is, 608MD is configured to react to MIDI CC #1 and #2. Those are Mod Wheel and Breath Control, respectively, which Cubase sends 0 to all MIDI capable plugins as a part of MIDI reset.

608MD reacts to CC #1, that is assigned to the Input knob in the default setting. Similarly, CC #2 is assigned to the Output knob, reset to 0.
I searched for an option to turn off MIDI CC completely but didn't find one.
Short of cutting the root, I assigned other MIDI CC to those two knobs from MIDI Learn. SUCCESS!

My 608MD stopped responding to MIDI reset to turn input and output down to zero any more.
I've saved this config to a file, and load it to every 608MD instance.

I'm using Cubase 7. Cubase can remember a specific config of a plug as the default of the plug, so I've made this CC config the default plugin setting. Moving forward, I should not have to worry about this reset issue any more, I can completely forget about it until I need to reinstall Cubase.

Folks at PSP Audioware, please, please don't assign those CCs to any knobs in the default setting, that are often observed to return to 0 (on real devices and on reset). Particularly, CC #1 and #2 are the worst combination to set to Input and Output by default.
I had to stop using 608MD because of this problem. I'm so happy to have found a solution, now I can use 608MD in real projects.


PS. I was willing to share the CC config file, but this forum does not seem to have file attachments. Please let me know if you have an idea how to post/share it.