I'm having similar problems. This just started happening recently for me; as in maybe a week or two ago. I'm using an Xbox 360 controller with the wireless PC adapter.

Since it's wireless, I thought the batteries were dying, or some other wireless signal was interfering, but after trying different batteries, a different controller, and re-positioning the wireless adapter, I found out the problem is just with FFXIV -- other games on my PC work just fine.

So frustrating. I'm really hoping this gets resolved soon.