Type about:preferences#privacy<enter> in the address bar. The button next to History, select Use Custom Settings.

Turn off Always Use Private Browsing Mode Turn on Remember My Browsing And Download History At the bottom of the page, turn on Clear History When Firefox Closes. At the far right, press the Settings button. Turn on ONLY Cache and Form And Search History leaving the others off.

Followed everything to the dot and still keeps logging me out.

A detail like a website remembering you (log you in automatically) is stored in a cookie.

You can use these steps to make a website recognize and remember you:

• you can create an allow exception to keep specific cookies, especially in case of secure websites and when cookies expire when Firefox is closed (Delete cookies and site data when Firefox is closed).
• Options/Preferences -> Privacy & Security
  Cookies and Site Data: Manage Permissions

• clearing "Site Preferences" clears exceptions for cookies, images, pop-up windows, and software installation and exception for password and other website specific data
• clearing "Cookies" will remove all selected cookies including cookies with an allow exception you may want to keep

It is possible that the cookies.sqlite file in the Firefox profile folder that stores the cookies got corrupted.

• rename/remove cookies.sqlite (cookies.sqlite.old) and when present delete cookies.sqlite-shm and cookies.sqlite-wal in the Firefox profile folder with Firefox closed in case cookies.sqlite got corrupted.

You can use the button on the "Help -> Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page.

• Help -> Troubleshooting Information -> Profile Folder/Directory:
  Windows: Show Folder; Linux: Open Directory; Mac: Show in Finder
• https://support.mozilla.org/en-US/kb/Profiles