The messages that you’re getting don’t *necessarily* mean that the firmware update failed. The “Firmware update appears to have failed” message in the Mac updater app is what you get if the programming sequence appears to have worked, but that there is trouble connecting to the board after. Likewise, the mphidflash messages suggest that the programming itself is going OK.
You might try manually resetting after the programming sequence finishes, or possibly disconnecting USB for a bit after. (You can and should leave power disconnected for _all_ testing until communication is working again.)
Your symptoms are also consistent with your computer being slow at recognizing a recently connected USB device, or having a somewhat slow/unreliable USB connection. You might try a different computer, a different port, or a different USB cable.
If you continue to have difficulty, it could be a hardware problem on the board itself. Which model of EggBot is this?