I am having the same issue.
  • Connection is an ethernet connection to a router
  • Windows Firewall and antivirus software are disabled
  • I get booted in Limsa Lominsa, Mists, instanced dungeons (coil turn 9 & Ramuh Extreme), etc
  • I checked IE settings, changed to Win 7 compatibility mode, ran as admin, restarted PC, rebooted modem and router, flushed DNS, tried different DNS servers, and tried without my router (connected directly to modem).