I'm not able to replicate that issue. If auto-select is unchecked it should stay unchecked even after closing and re-starting Photoshop.
You could try resetting preferences Preferences in Photoshop
If that doesn't fix the issue, you may need to uninstall and reinstall Photoshop.
Check the permission your userid has for its Photoshop preferences folder. It sounds like when you close down Photoshop your current settings are not being saved.
I'll try both suggestions. Thanks very much for your responses.