I had this issue for a very long time,
This is how I fixed it: I started the game, went to setting and set my custom keybinds (for bebop i.e.) then went and changed some other setting (audio/video), went into sandbox mode tested then keybinds, then went back to mainmenu, reverted the audio/video settings, then exited the game from the main menu. when I opened the game again the keybinds were saved.
couple of days later, I faced the same issue when setting custom keybinds for lash (bebop's were still saved), so i repeated the same steps above and was able to successfully retain lash's new keybinds,
I hope this works for you