As Trey Jackson said, you want to put this:
(savehist-mode)
in your Emacs start up file, then restart Emacs. (Calling it interactively will stomp on your current mini-buffer history, so you may not want to do that.)
It’s also worth pointing out that you can persist other variables across sessions by adding them to savehist-additional-variables, like so:
(setq savehist-additional-variables '(kill-ring search-ring regexp-search-ring))
You may also want to customize savehist-file, to pick the location where Emacs saves all this stuff:
(setq savehist-file "~/.emacs.d/tmp/savehist")