Hey, good question.
My plan is for the game to reach a beta state at some point, from that moment it'll be possible to maintain save game compatibility.
When is is beta? Whenever all characters are implemented and their stages and events have caught up to each other.
You know, another idea came to me a couple days ago...
What if there was some sort of cheat code, similar to the "Get More Money" option where you could bring certain characters to any given point in their stories, which could be a way to continue the sort from where you left off in the previous version. I imagine that you could give a prompt before the game starts asking whether you have played the game before on a previous version or not, and this cheat would only be available to players who answered yes to that prompt.
A simpler solution could be to give an option as to which week players want to start at, and put all of the characters into the stages they would be at the point the players choose to start.
Also, I know this might be prying at things I probably should not know about yet, but just how many characters ARE you planning to put in the game? There's already quite alot, with some more on the way that have been hinted at. (Ive gotten to week 45 or so, and I'm pretty sure I've done all the unique events by this point, seeing as I've gotten all the characters to their highest stage for v0.9)