I'll make this nice and short as this is happening way too much.... It happens a lot, but seems very random to why, so it cannot be force replicated on my end.
1) Enter Mission... mission takes forever to load then "Server Not Responding" in red shows up. Sometimes this goes away and the mission loads as intended, othertimes, you get bumped to login (not launcher).
2) Try to reconnect, you get to the login screen, character select loads fine.
3) Click PLAY and bam "Game Server Connection Failed".
It will keep saying that until almost 10 minutes passes, when I assume the character is auto logged out. IT's been happening a lot recently and is REALLY starting to get annoying... and it's not just me. In a group mission, this happened to myself (NoVA/DC area) and two friends (one in Chicago, one in South Florida).... so it's not a regional or ISP issue.
It seems like there is a bugged exploration mission from what I've been seeing. You enter that mission and your characters gets stuck in no-mans land. After ten minutes of being logged out the misson resets and you are clear to roll another mission. I wish I could figure out which mission so I could submit a bug report.
Happened very frequently to me yesterday. Most notably, I was in a mission, and after going through the initial space battle, I was to beam down to the system's surface. During the beam-down, it gave me the "Server Not Responding" stuff. I tried logging on over and over again, and finally it let me back in, but it had spit me out of my mission and back on the map. Luckily, it gave me the option to re-enter the mission and go directly to the surface of the system.
Hopefully these scheduled maintenences are fixing the issue. I'll find out once I get home from work and can play.