I had this issue, posting what I had to do to solve it here in the hopes that it helps you guys too..

I play with a ds4 and i've had this issue in the past - buying a new cord to plug it in solved it at the time. Fast forward a few months..and after a computer reboot the issue reared it's ugly head again, so I set out to figure out how to fix it. After searching this issue and finding a shocking amount of people also experiencing it online, a common theme was popping up - device manager refreshes. The big culprit with these is usually a device disconnecting and reconnecting(often USB), so I found a piece of simple software online called usblogview which you can use to see usb devices disconnecting/reconnecting.

Sure enough when I had this software open and tried to play ff14 with my ds4 I immediately noticed my USB-SERIAL CH340 was dropping and reconnecting on a normal basis, so I went into device manager and tried disabling this function (as far as i know it has something to do with my in case lighting system) and the moment I disabled it my problem was immediately gone and I once again enjoy interrupt free gamepad play.