Whenever I plug in another keyboard, key repeating rate is reset to some value

I solved the same problem by editing my ~/.xserverrc.

It looks like this:

exec /usr/bin/X -nolisten tcp -ardelay 300 -arinterval 25 "$@"

It's equivalent to xset r rate 300 40, because xset uses frequency while X startup options use a delay (1000/40Hz = 25ms). In your case ardelay would be 250 and arinterval would be 10.

Note that I'm using startx to launch my X session but your display manager (if you use one) might not read your xserverrc. Gnome also seems to override the rates even when launched with startx.

I am using a USB keyboard that is attached to my laptop so I doubt PS/2 is related to this.