Hi Guys,
I had this issue about the same time all you guys did. I did some research and my findings are below.
For those who have this issue, open "Device Manager" and let it sit there. Next open the game and go into windowed mode so that you have the game and device manager next to each other.
Now, play the game for a bit and if you notice, every time the controller goes crazy, device manager should "blink" or refresh. If this doesn't happen to you, then no need to continue from here, your issue isn't my issue that caused this.
If you did notice the "blink", then we're having the same issue, such that every time the device manager refreshes, we lose controller responsiveness, but our characters keep moving, or buttons don't respond and yes... if you were tanking Titan Ex, you just ran of the edge. So let's fix this issue (and I must say, I still think there is some code issues in the game that need to address this, so consider this a "workaround").
The thing you need to now do is track down what is causing your "Device Manager" to refresh. To do this, is a long and lengthy process, but to get rid of the "obvious" go a head and update all your drivers to make sure you have latest. Once that is done, if you are still blinking, then you need to expand each tree element and note down the devices that are there. The "Blink" should add or remove one of these every time it "Blinks". You must keep going through all the items here and wait for the "blink" to occur and make sure that the item you looked at didn't disappear or reappear. Once you track this down, you need to figure out a way to disable it.
For me, it was actually because I was running "PlayOn" which is a DLNA streaming service and located under "Software devices" in device manager. At some point in time, Microsoft pushed an update that "PlayOn" wasn't happy with causing it to constantly crash and refresh my device manager. Stopping the PlayOn service fixed my issue. Now, there are a lot of other ones out that that behave the same way, so your PC is most likely different.
NOTE: There may be more than 1 issue in your device manager, so if you know what all the items are, you can disable everything until it doesn't refresh, then re-enable and see what is causing the problem also.
The real problem... (hopefully SE reads)
I think FFXIV has a device enumerator such that every time a device is connected it triggers the controller code to see if FFXIV has to change controllers. Somewhere in that code, it stops responding to the currently connected controller while it determines if it has to switch controllers. Not sure how to log a bug, but being familiar with how software is built, I am fairly sure this is what is "truly" happening.
Anyways, this resolved the issue for me and I hope it helps all of you. It answers all the basic questions like why it was so sporadic.
Good Luck!