GRUB – Remember last choice

All variables in /etc/default/grub start with GRUB_, so the correct syntax is GRUB_DEFAULT=saved, not DEFAULT=saved.

The official grub manual describes this correctly.
Put the following in /etc/default/grub:

GRUB_DEFAULT=saved
GRUB_SAVEDEFAULT=true

Then run:

sudo update-grub

Ref: https://askubuntu.com/questions/148662/how-to-get-grub2-to-remember-last-choice