Using the Arduino serial monitor seemed to keep the Bluetooth 'connected' LED steady, and I could more easily upload code. But I had to use the USB connection to get to that point. It was all very 'hit and miss'.

Update - After many tries, I managed to get the Bluetooth connection connected long enough to get the Arduino serial monitor running. With the monitor connected, the Bluetooth connection stayed connected long enough for the sketch to upload correctly. Now the Ultrasonic sensor is working properly.

I'm still having problems maintaining a Bluetooth connection on the Mac. I have now tried using the Arduino app and I am having the same problems as the OP. The connection breaks before a sketch can be uploaded. I've tried altering the distance between Nybble and the Mac, but that seems to make no difference. It did work once and the Arduino serial monitor was receiving data, but the Ultrasonic sensor was not working properly - always showing 1 or 2 cm. Subsequent attempts to upload the sketch will not connect. Until I find a solution I will have to go back to the USB connection, which does work.

I tried forgetting the bluetooth connection on the Mac and reconnecting - no difference.

I have a similar problem on my MacBook - the bluetooth for my Nybble announces as BittleSPP-8775CF. Never Nybble - I'm not sure that matters, but it won't stay connected when I use the desktop app, and the only way I can use the app is through the USB serial link. My Android phone has no problem keeping connected.