Hello, my name is Rusty. I'm a sound engineer, and chasing "ghosts" in the power can be a bit of a headache. If power goes up a midi line, it will confuse the midi signal and you'll have to mess with it to get it back. It's basically like exiting and restarting the process.
To deal with dirty power, you should plug into a transformer. This cleans up the power and conditions it for our audio gear. The popular model is a Furman, click here. This is on top of all of my racks, and it gets rid of the line noise that gets absorbed due to dirty power. Give one of these a shot, it should fix the problem. Since it works at other venues, I have my sights on dirty power at the venue.
Well, do you generally plug into the same power source for both devices? Power conditioners make a loud noise when they go bad. Have you tried another power outlet at that venue? Stages will usually have 2-3 circuits.
The Furman is supposed to take the place of the power strip. Power strips are wired sometimes backwards, poorly, etc... Most of them are cheaply made. Use the Furman as your power strip, and you will have the best chance of solving the problem.