This just happened to me as well. I have not tried other characters, but when I loaded a single mission it said "server not responding" however the mission eventually loaded. When I entered into another mission it said the same thing but I was booted before it loaded. Now I cannot access that character at all when attempting to log in.
UPDATE: This was resolved for my account and is working fine now. Took about 15 minutes.
I am having this same problem now just trying to enter the Kei system on the first patrol mission outside of the Sol system. I'm guessing it might have something to do with too many players trying to use a cluster at the same time and the server is just dropping random people when this happens. Wish Cryptic would give an update as to what causes this and an ETA on a fix.
I'll add my own person as experiencing this problem at the moment: trying to enter the Great Bloom system when I first get a "server not responding" message during the loading screen, then a connection to server lost message...