As for what the error message means, it's a Windows error box that shows up, telling me that Java SE Platform Binary has stopped working. It's not an error message from MapTools itself. This only happens while connected to a server.
As this issue is a significant outlier (in fact, I've never heard of this particular error as presented)... I would usually just assume that it was a bad Java install. But as you've already reinstalled, I have to think that there is something more particular to the system running the application that is the problem.
You could check to see if the computer could be restored to a point previous the having the issues (try to go back 4 weeks or so if you can). That might put the system in a state previous to some new software installs or updates.
Also, as it is something that crops up only when a server is running, I think I would start by updating and re-installing all drivers associated with the motherboard.
If you have the motherboard model number I could suggest what drivers, specifically, I'd update and provide links.
And then I'd follow up with a clean install of Java and MT.
As far as hardware goes, the network card could be going, or a memory stick, or some other component on the motherboard. This isn't the most likely possibility, but if you can't address the issue with software you will have to start looking at the hardware more closely. Can the server use a wifi connection or a different network controller to test?