Does it happen when you use Fullscreen mode in the Display menu? (Change display mode from Windowed, Borderless Window mode to Fullscreen).

You can also try changing the Effects in use during combat by:

Main Menu > Character Configuration > Control Settings > Character > In this tab here, scroll down and change the Options for Battle Effects Settings, from the default which is Show All, to Show Limited or Show None.

In Raids for example, this will greatly help with FPS as you can turn off Party and Alliance player Effects in that menu that I noted above.

Hopefully that will give you higher FPS and stop the drops!