I took mine into the Marina on our lake (an alleged Mercury Authorized dealer). The first time (after they had it for a week) they said the ECM stored a "low-voltage" code which they were able to clear. They also checked all the connections. I got it back and the first time out, it did the same thing three times (shocker). I called them back and told them they did not fix the problem. I brought the boat back to them for a second look. This time they had the boat for four weeks. Finally, when I got it back, they said that everything still looked good and they could not find the problem. The ECM did not show any code hits and they could not recreate the problem when they were testing it. They said they had the boat hooked up to a computer while they tested it in the water, at several different MPH & RPMs. Basically, I was told their best guess is that it is something electrical where a wire is disconnecting or shorting causing the boat to reset as if you were turning it on for the first time. The only way they could truly diagnose something like that would be to pull all the electrical wires out and test them one by one, which of course would cost a fortune in labor, and even still it might not solve the problem. They were pretty certain it was not the ECM.
So, after getting the boat back a second time, the issue has only happened once. It has never happened at a low speed or RPM (5 mph or less), for me it has always usually been between 11 and 15 mph.
At this point, I have decided to just deal with the issue. If it continues to happen next summer, I will just trade the boat in and get a new one. Sorry, I don't have a definitive answer for anyone, I wish it was an easy fix but it sounds like it is the unicorn of all motor issues. If anyone gets a clear answer or fix, I would love to hear as well!
Good luck!