The team at CCP appears to be aware of the connection issues that some people have been experiencing.
It seems that if your connection is routed to them via one of the ISPs that CCP uses, LimeLight Networks, you may have experience the whole disconnect problem.
CCP says that they have turned off their connection to LimeLight, which should make the problem go away, and has requested answers from LimeLight. LimeLight took the position that it wasn’t them but somebody up stream from them causing the problem.
CCP has a post about it here in the EVE forums, which is followed by the usual measure of responses from people who feel they know better, are willing to speculate and start rumors, and those with poor reading comprehension skills.