I'm having the same problem with my SD card. Been working perfectly for a couple of months, and then as soon the update to Kitkat had completed, I had a message box warning me that the SD card was removed without unmounting. rebooting or removing and reinserting the card fixes it for a while, but it always disconnects again within a few hours.
I'm running stock, not rooted, and the SD card is a "Samsung 32GB Class 10 UHS-1 Grade 1 48MB/s MicroSDHC Plus Memory Card"
I have tried, erasing the SD card using the option in settings, resetting and erasing the device using the option in settings (am I right in thinking that is a factory reset), and then erasing the card again.
I'll try a different card over the weekend, and consider rooting...