@kylelanman
I wish I could definitively answer your questions, but there is much more that I don't know than I do. Here are my best guesses:
I think Eric H. is correct above in his description of the alliance station light. This light is different this year than in previous years. You want this solid. I'm not sure what controls it specifically, but it has a different flash pattern than the Robot signal light.
The robot signal light is discussed
here. Once again you want this on solid. In finding this document I was reminded that there needs to be a jumper installed for the amber light to accurately reflect the LED status on the digital sidecar.
The classmate is able to exchange packets with the robot prior to match begin. FMS will not allow a start with robots not ready. If a robot-DS connection cannot be made, your robot can be bypassed to enable the match to begin, but at events where I have been, you would know that was the case before the MC begins the countdown. So what we need to know is why your connection dropped.
I'm guessing based on your screen name, but assume that you know something about what a non-routable network is. This is essentially what an FRC field is. This is why if robot communications fails to just one robot, the culprit is most likely either on the robot itself or the classmate and its individual ethernet cable. A failure in the rest of the wiring loop would most likely affect multiple robots.
I do not know how the classmate is controlled by FMS. I think it is most likely detecting the presence of the FMS and then behaving slightly differently, but I'm not certain. At first glance, I'd try to do it this way since once the match is started, packets to and from the robot are then handled only by the communications hardware (router, switch, access point) and not through any upper level software program (which could reduce bandwidth). It would be simple enough to have the driving program on the classmate poll the FMS every 100 ms or so and enable/disable as required. Of course, that might not be how it is really implemented.
I'm not a big fan of Windows*, especially on underpowered devices, so I'm not happy with the boot time and other idiosyncrasies of the classmate. However, it's much better than last year's blue box of death. I have a laptop that forgets it has a DVD drive every time someone closes the lid, so I'm not sure I'd recommend your logout/login regimen. We've already heard reports that USB connections can get wonky in certain circumstances. I think there are issues we are still uncovering as our first season with this device unfolds.
I'm pretty sure you can't connect with the field if your classmate is logged in as developer. You may have been able to have the same effect by simply logging out and logging back in. I've heard that it is necessary to do this after each match to clear the FMSlock.
At your next event, please check with the FTA early on practice day and let him.her know what you have experienced so far. Perhaps by that time more answers will be available.
At my next scorekeeping event, I will be taking even better notes about what is happening and what our best guess is regarding the causes. Hopefully this will help improve gameplay for all teams.
* I am an IT guy IRL, so please spare me the flame war. I haven't met the perfect computer/OS/programming language/DBMS/app/etc in over thirty years of working with them, so let's just focus on making what we have better, ok?