For what's it worth, here's what I've learned on all-terrain vehciles and motorcycle GPS power issues. The most common problem is "vibration induced shutdown". Most newer Garmin GPSs have a chip running inside (Intel 386 or ARM) which can get confused and shutdown, or freeze up, if the 12V power supply is not smooth and steady. If the GPS is hardwired to the 12VDC supply and you are still getting shutdown, try these things:
Eliminate any possible source of disconnection under vibration. No spring-type fuses, use a blade-type. Tap directly into the 12vDC supply if possible. If using a cigarette lighter socket on the bike, that connection is a likely source of the disconnection. Use tape or clamp to immobilize it. Use dielectric grease on the all contacts and connections. Especially if using the spring-type fuse holder inside the Garmin cigarette lighter adapter. Take the fuse out and put dielectric grease on every little part in the power path. Sparking can contaminate the connection points. Once you've contaminated the metal coatings on the terminals (or sanded it off), the contamination gets worse. I'm not familiar enough with the H-D (Garmin OEM) interconnects, but it sounds like a vibration shutdown type of deal.
I've run the Garmins with HDD (2620) and isolated the mounting some along with trying to reduce the connections to the minimum. So far it's been pretty good aside from when idling or low speeds and the associated voltage drop kicks in.
Good luck !!