I have been experiencing numerous lost connections to the final fantasy servers since purchasing the game a few weeks ago. In all cases my internet has been fine for other games/activities.
I have solved the lost connection issue and thought my solution may be of use to other players. The network I was connected to (my home network) had been classified as a "public network" by Windows 10. By changing the network classification to a "private network" my disconnect issues were solved. I do not know if other versions of windows will effect the game the same way. I hope this is helpful for someone!