[TeutonicNight]

I noticed that in the logs from Sunday, the DS is reporting being disabled the whole time, and the robot keeps switching in and out of disabled. Maybe that is completely unrelated to the problem or something, but when we were at our Regional, like Bob said, our robot was also having connection problems, and for one match we couldn't move at all - and when I looked at the logs, our DS was also reporting to be disabled for both matches, except for the very end of match 39, when we suddenly gained control again.
Match 39 was a very strange match, because another robot on our alliance was having problems connecting to the FMS and we not only had to wait a long time for the match to start, but we also disconnected and connected to the FMS a few times. Match 39 for us also looks a lot like both logs from Sunday for you.
We were not the only team at the Regional to have connection problems, and the other teams with connection problems were different from us in may ways. I have been trying to get down to the root of this problem so our Regional is not stopped by this again next year, and I've narrowed it down to a few things (though I am new at this, so there's definitely room for error)
1. A problem with the FMS (which would not explain your problems, so it seems less likely)
2. A problem with Drivers Station (which could explain your problems too)
3. A problem with the roboRIO (which would not explain your problems again, but maybe they've stemmed from different things)
4. A problem with too much interference, bandwidth, or related (regionals are very busy, and you said the place you were demoing at had lots of interference)

Again, maybe our problems are from completely unrelated things, but the logs and the problems themselves seem pretty similar, so maybe we could help each other a bit.

*When I looked at the log again I saw that we got a "code start notification" twice, and after we would get them we could move, but we stopped again after the first one - something your log didn't show. Maybe our problems aren't as similar as I originally thought...