The stereo socket should have been removed long ago, prehaps it's time for a mini USB connector. USB capable Picaxe.
While I do not particularly care for the stereo connector, I like mini/micro USB connectors even less. I have quite a few devices with mini/micro USB connectors and after being used a while sometimes the connector must be tweaked/jiggled to work. IMO they just don't hold up very well. The stereo connector works well in an educational environment when the socket is soldered onto a project board. However on a breadboard it can be a real pain. I have several AXE027 cables, one is unmodified and used with project boards that have the stereo socket. The other has the stereo plug removed and a three pin header socket installed. This cable is used for manufactured boards and breadboards where a 3 pin header is used to save board space.
The recommended download circuit of a 22K current limit resistor and 10K pull down resistor seems to be a throw back to the days of RS232 signal levels that can be as high as +15/-15V. But, with a 5V supply and an AX027 which has 5V I/0 levels, the 22K resistor is really not needed at all. However, many of us operate the Picaxe at lower voltages, such as 3.3V or even lower. In this case, for the internal clamp diodes to work effectively it is necessary to use a current limit resistor. Any value from 330R to to 22K will work fine and make the Picaxe "5V tolerant". When using an AXE027, and where there will never be RS232 voltage levels, I generally use a 1K resistor to limit the current to about 5 ma.
I would however, like to see a cable made available the brings out the USB 5V, that would allow powering a breadboard or Project board from the USB port. For now I just make my own if the need arises.
NOTE: If using and RS232 connection/cable it is important to use the 22k Resistor, which in effect, limits the current into the serin pin to about 600ua.