How time flies!
My first solution to the problem of my unprogrammable Arduino bit was to purchase a new Arduino bit - and that certainly worked! But it's not a cost effective solution, so I have followed every thread here and elsewhere about 'disappearing ports'. Lots of ideas, however none ever solved the problem with my bit. Until now!
I found a solution, described in reply #1 of this thread on the arduino.cc forum.
I have been able to rescue all of my locked-up 32u4 boards using the method described: reset-upload, reset-upload, ... repeating until the upload catches. Do not wait for the port to appear, if you do, it will be gone before the uploading actually begins. The way to catch the short time the port is available (a few hundred milliseconds maybe?) is to just keep resetting and immediately uploading from the IDE. Use a short program that uses few resources, such as a modified Blink sketch, where pin 13 is replaced with pin 9, and one of the LED bits (led, brite led, long led, uv led, rgb led, bargraph, or a number bit) is attached to the middle output connector.
Then you'll need to attach a switch - a bare component or even just a wire, not the button or other switch bit - to the appropriate holes in the ICSP connector on the board. See this recent post of mine about how to do that.
Next, open or create your simple sketch in the IDE. Use the version 1.6.11 or later. Notice that the Board Manager (in the Tools > Boards > ... menu) now has a littleBits Arduino Module option. Select that as your board. Compile (ie Verify) your sketch, and be sure that it compiles correctly. Then poise your mouse over the Upload button. Contact and release the reset button you made, and click the Upload button.
If the program uploads - Great! The Arduino is freed and will now function normally. If you get an avrdude error that there is no port, or no device, or other hardware error, wait a second or two and do it again. I needed to repeat the process 9 times to get my Blink sketch to upload to my previously 'bricked' Arduino bit. After that sketches uploaded the first time, and the port appeared in the Port menu