Specifically, the "mini" is a kk2.1.5 board, shrunk. Any kk2.1.x ROM will work -- a Google of "kkmulticopter flash tool" should link you to the software tool that can drive a USBASP for reprogramming.
This won't fix your failsafe issue, however. ALL failsafe functions reside in the RX. The "failsafe" loaded in many flight controllers is code to respond when the receiver goes into it's disconnected state (which is the failsafe, if the RX supports it). If the RX's disconnected state is to continue to send the last signal it's received, the flight control board has now way of knowing the RX has lost contact . . . and off it drifts on a voyage of self discovery
In either case, the "Failsafe" in any of the kk2.x boards is "fall out of the sky". As bad as this sounds, it's probably the safest way to go. the longer the props spin without a pilot in command, the farther it will drift, increasing the chance of a damaging crash or outright fly-away. I'd rather have to pick up broken pieces than have no pieces left at all . . . or worse, rush someone to the hospital.
If you'll hook up your RX, removed the props, arm and throttled up, then turned off your radio, whatever the airframe does next is what it will do in the air if the radio link is lost. If you can't live with that, I'm afraid in this case you're better off replacing radio gear than the flight control board.
