GTA V Doesn’t save my progress after I log out

I finished the mission where Trevor blows up the trailer park with “The Brothers...”. Then head over to Los Santos at the new Safehouse, I go sleep to save manually. I then SWITCH to Franklin and do 1 mission wherenI help Tonya again to tow a car. After that, I head home to sleep & save manually and switch off the console. When I switch on again, to play, after a day or two I’m right back to before before destroying the O’Neils’ meth house. Why is this? Why won’t it save my progress? I play GTA V with a storage device and save my progress there.

GTA V has an autosave feature, or rather, it prompts you to manually accept a save whenever it triggers. Thing is, if you reject it, it turns off "auto saves", and they must be re-enabled in the Settings Menu.