can't save the game

If you're playing on PC, your game should be saving to the folder below:

C:\Users\**USER**\Documents\Need for Speed Heat\SaveGame\savegame

If you're having these issues, next time you're exiting the game, go into that folder and make a copy of the "1" file in any other folder (has to be a different location). If you find that the game resets, try importing your duplicate "1" file back into the original "savegame" folder and over-writing the 0-progress save it starts you off on. 

I'd imagine it's a similar process to backing up the save, so I think it might help you.