I've noticed another behavior which hasn't been noted anywhere above: after my joystick disappears, I can often make it re-appear by going into Configuration>Video and switching between fullscreen and windowed (or using Alt+Enter). I've also had it reappear coincidentally when I changed other settings (like cycling between Low and Ultra on the texture setting). It's not 100% reliable, but it looks like making the (rendering engine?) restart allows the game to successfully refresh the available devices.

In case it makes any difference: running Windows 8.1 and a MadCatz FLY 5. Mainboard is an Asrock Z77 Extreme 4, and I even got a discrete USB controller in the hopes of it helping the issue (Inateck USB3.0 w/ 2x USB3.0 and 1x 19-pin internal)

Edit: Is it not possible to continuously poll for new controllers? It sounds like that would at least help to mitigate this issue.