In some cases, hosts will set a limit on the amount of memory WordPress can use, and this can cause certain issues, like the Customizer not being able to save or even load (just shows a white screen).
There』s a couple different ways to increase your memory limit.
Easiest Method
Just ask your host – they』ll more than likely be happy to increase your memory limit.
Edit wp-config.php
The WordPress Codex has an article on this here.
Find your wp-config.php file in the root of your WordPress installation by using FTP.
Then add this to it:
define('WP_MEMORY_LIMIT', '128M');