Beta and regular uses the same local appdata folder. Which is stored under the Local application folder in windows.
Uninstalling either beta, live, or both should not touch these folders.
That contain graphics settings, and binds etc.
I also rather suspect that missing bind files is not so much a matter of the game deleting a file.
Even the "custom" bind file gets a version numbering on it, and I believe ED looks for the most recent of those.
But rather a notice that one of your devices has changed ID or name.
If Elite finds a bind file using an ID of a device no longer connected, it will completely ignore that file.
Forcing you to having to re-bind all keys.
It shouldn't happen too often but some devices, particularly older, doesn't send a simple identifying name. Leaving windows to use its own method to generate names for it, that also includes the specific port is connected through.
So just moving ports, hubs etc around could trigger Elite into thinking its not the same controller and invalidates your binding.
I have even had devices change ID on me from just rebooting.
Because I plugged them in one order, but as my computer turned on it activated ports in a different order.
But this is a rare occurrence these days.
I do recommend renaming the "custom" file generated when you make a new or change any default bind files to have a better name, this would also preclude ED to replace it.