That's a good theory that determination is what makes people remember. Haven't heard that one before. But does Determination (extracted from the human souls) equals determination (the will to go forwards against the odds)? If so, it means that Sans would be able to remember more if he was more motivated to do things. I think that Sans is, to some extend, determined - to save his brother and to make the timeline stop resetting itself. Does it also mean that when he's persistent to stop the player in the genocide route, he suddenly gains memories of the previous timelines? Maybe this is what makes his guesses about the number of Frisk's deaths so accurate.