I might have figured out how to solve the problem but I'm not sure yet.

What's going on is I'm saving over the initial "new character" save that automatically takes place after you get off the carriage at the execution. I tried now to save in a new game slot and keep my "new character" save, because that one seems to keep being overwritten if I save over it and make a new character later. If I don't quickly backtrack, I lose my old character's auto-saves and ultimately they are deleted for good.

I've tried making two new data saves which seems to have fixed the problem. So should I just avoid saving over the "new character" save from here on? Has anybody else had this problem? I used to play this on the Xbox 360 and it never happened when I saved over the "new character" save.

Just Bethesda being goofy with the PS3 version as always. The manual save shouldn't be deleted. The ones that are deleted are the autosaves. To make sure, next time you start a new character manually save twice.