I am also encountering this.

Platform? Windows
Which controllers specifically did you try? 8BitDo Pro2 in X-input mode.
When using wired method, did you disable any bluetooth options to avoid interference? Yes.
Do you have multiple controllers or other 3rd party devices hooked up the machine? Not multiple controllers, many other 3rd part devices such as audio interface, mouse, keyboard.
Did anything change in the computer's environment that may have contributed to the problem? Not that I am aware.
Try running a clean boot on the machine to see if that may help (disable any programs that may be interfering with the game such as discord if applicable) issue has persisted for a week across multiple reboots and environments (computer has moved)
Wired or wireless connection:
Internet Service Provider: Comcast.

Additional info: I had https://gamepad-tester.com/ open on another screen during gameplay and it did not encounter any dropped inputs while FF14 became unresponsive as the same time. Because of this, I am not inclined to believe it is the controller's fault.