*different* Safari logs me out halfway through browsing

1. Delete Caches.db

Close all windows and quit all applications.

Hold "option" key down and click "Go" menu in the Finder menu bar.

Select "Library" from the dropdown.

Library > Caches > com.apple.Safari > Caches.db

Right click the Caches.db file and select "Move To Trash".

Close windows.

Restart and relaunch Safari.

2. Delete com.apple.Safari.plist file and test.

Empty the Trash.

Quit all applications.

Hold the option key down and click the "Go" menu in the Finder menu bar.

Select "Library" from the drop down.

Library > Preferences > com.apple.Safari.plist

Right click on it and select "Move it to Trash".

Close the Finder window.

Restart. Relaunch Safari.

If this doesn’t help, “Put Back” the com.apple.Safari.plist

Right click on the Trash icon in the Dock and select “Open”.

Right click on the com.apple.Safari.plist and select “Put Back”.

Try a restart.

Do a backup, using either Time Machine or a cloning program, to ensure files/data can be recovered. Two backups are better than one.

Try setting up another admin user account to see if the same problem continues. If Back-to-My Mac is selected in System Preferences, the Guest account will not work. The intent is to see if it is specific to one account or a system wide problem. This account can be deleted later.

How to test an issue in another user account on your Mac - Apple Support

If the problem is still there, try booting into the Safe Mode using your normal account. Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up after waiting 10 seconds. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application un-installer. For each disable/delete, you will need to restart if you don't do them all at once.

Try safe mode if your Mac doesn't finish starting up - Apple Support

OS X Yosemite: Start up in safe mode