Puck.js automatically disconnects after sending code - nothing stored though

To test my code I do have to connect it to my PC as a keyboard

Well, if you don't want to physically touch your Puck then yes, to debug you have to be connected via Bluetooth.

But it is possible to solder on a UART connection, then you can debug and reprogram via the UART while being connected (possibly to a different computer) by Bluetooth: http://www.espruino.com/Puck.js#serial-console