When you make changes to the keyboard or mouse via Preferences>Keyboard and Mouse; the changes are saved in 2 files name "sms" for the mouse, and "sks" for the keyboard. These script files are then run to set the mouse and keyboard settings. Problem is that they are NOT run at each boot so the settings are not remembered.
To fix this myself, I added a desktop file to the autostart directory to run the sms script file (I dont have any custom keyboard settings). Desktop files in the autostart directory will run at each login. The autostart directory is located at /home/yourhome/.config/autostart, for "yourhome" being your own home directory name. The autostart directory was not created by default, so you may need to create it (use pcmanfm, right-click, create new-folder....).
!st, go ahead and make your mouse changes via Preferences>Keyboard and Mouse to create your sms file.
The desktop file I use is pasted below, make sure you replace "yourhome" with you actual home directory name. The Exec line is the important part of this file, it is what runs the sms script file:
Something else odd is that if you run Keyboard and Mouse again, the settings are not reflected there either. The mouse-keyboard application could probably use some minor improvements in this area.