Someone already filed this bug, but it's still a bug and still not fixed after nearly a year later...
forums.garmin.com/.../bug-ant-control-function-5-and-up
I narrowed it down to when I map the blips "combination" function. The Edge 1050 mistakenly allows you to configure a "long press" for a combo blip press which isn't supported by AXS blips. When I try to configure anything on the Edge 1050 firmware after adding the blip combo, the firmware won't allow.
The other issue is if you map functions out of order, the Garmin doesn't see the new functions. For instance, if I map AXS Function 1, 2, and 4. The Edge 1050 will show Function 1, 2, 3, 4 when no "Function 3" exists.
There seem to be a number of bugs here.
(1) configuring a blip combo mistakenly allows a "long press" configuration
(2) after a blip combo is mapped to AXS function, the Edge 1050 glitches out and won't persist any changes to the function mapping.
(3) previous AXS functions can't be reconfigured after the blip combo function. They can be changed, but if you load them again, they'll revert back to the previous values.
I went as far as clearing out my AXS pairing, and then re-pairing every component with the new firmware. But, the Edge 1050 still glitches out after I configure the blip combo function.