Akeeba LoginGuard requires PHP 7.1 to work, as documented on its download page. In fact it checks your PHP version before installation, preventing you from installing and using it on sites with older versions of PHP where it'd break (it actually uses Joomla's pre-installation script system to check the PHP version and signal that the installation needs to stop if the PHP version is too old). If you drop your PHP version to 5.6
after installation it no longer works. Since it runs on every page of your site it will break your site. That's normal and expected.
Regarding what you did, you said "the plugin" but based on the error message you got you have either disabled just the component or just the user plugin. That's not enough or recommended for that matter. You need to first read the
documentation on how Akeeba LoginGuard works.
As you now understand, you need to unpublish both the system plugin (System - Akeeba LoginGuard protection) and the user plugin (User - Akeeba LoginGuard protection) BUT NOT the component. When you have upgraded PHP back to 7.3 you can re-enable these two plugins.
Note: on the Plugins page you can search for "LoginGuard", select both system and user results and click the Unpublish button in the toolbar. This disables both plugins at once, making sure you won't get any accidental problems if you try disabling them one at a time (not that you normally do, but better be safe than sorry).
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!