Thank you for the update Riko_Futatabi.

Based on this information, it looks like your disconnections come from a hiccup in the connection between you and the server. This would explain why you have no real issues until you abruptly disconnect (kind of what is shown in your second image). Unfortunately, this makes it a bit difficult to figure out where the issue is come from as you trace route would suggest that you don't have a problem at all.

What kind of area do you live in (urban, rural, etc.)? What kind of internet is your ISP (DSL, Cable, Satellite, etc.)

We hope we can be of assistance in helping you enjoy the exciting world of Final Fantasy XIV!